NPB Model for Birth Weight
Sheena Martenies
02/10/2021
#' -----------------------------------------------------------------------------
#' Install the new version of the package
#' -----------------------------------------------------------------------------
#library(devtools)
#install_github("lvhoskovec/mmpack", build_vignettes = TRUE, force = TRUE)
library(tidyverse)## ── Attaching packages ─────────────────────────────────────── tidyverse 1.3.0 ──## ✓ ggplot2 3.3.3 ✓ purrr 0.3.4
## ✓ tibble 3.0.6 ✓ dplyr 1.0.4
## ✓ tidyr 1.1.2 ✓ stringr 1.4.0
## ✓ readr 1.3.1 ✓ forcats 0.5.0## ── Conflicts ────────────────────────────────────────── tidyverse_conflicts() ──
## x dplyr::filter() masks stats::filter()
## x dplyr::lag() masks stats::lag()library(lubridate)##
## Attaching package: 'lubridate'## The following objects are masked from 'package:base':
##
## date, intersect, setdiff, unionlibrary(haven)
library(readxl)
library(mmpack)
#' For ggplots
simple_theme <- theme(
#aspect.ratio = 1,
text = element_text(family="Calibri",size = 12, color = 'black'),
panel.spacing.y = unit(0,"cm"),
panel.spacing.x = unit(0.25, "lines"),
panel.grid.minor = element_line(color = "transparent"),
panel.grid.major = element_line(color = "transparent"),
panel.border=element_rect(fill = NA),
panel.background=element_blank(),
axis.ticks = element_line(colour = "black"),
axis.text = element_text(color = "black", size=10),
# legend.position = c(0.1,0.1),
plot.margin=grid::unit(c(0,0,0,0), "mm"),
legend.key = element_blank()
)
# windowsFonts(Calibri=windowsFont("TT Calibri"))
options(scipen = 9999) #avoid scientific notation
set.seed(123)1 Exploring the data set
The HS data set was previously used in the CEI paper (Martenies et al., 2019). In the original analysis, we used an exposure index based on the CalEnvironScreen tool. We observed lower birth weights and lower adiposity associated with higher index scores, driven largely by exposures to social indicators of health at the neighborhood level. Now, we are aiming to use methods for mixtures to try to identify which exposures are driving these association.
The complete data set for the birth weight outcome consists of n = 897 participants. This represents 77.93% of the original Healthy Start 1 cohort.
Of the 897 participants, 27% identify as Latina, 17% identify as Black, and 27% identify as another non-NHW race or ethnicity. The median age of mothers in this dataset is 28 years. 51% of babies born were male.
1.1 Effect of year on birth weight
The following examines whether there are trends in birth weight by year of birth.
plot(hs_data1$dob, hs_data1$birth_weight)
abline(lm(birth_weight ~ dob, data = hs_data1), col = "red")
Grouping birth weights by conception year doesn’t show much of a trend:
bw_trends_by_concept <- ggplot(data = hs_data1) +
geom_boxplot(aes(x = concep_year, group = concep_year, y = birth_weight))
bw_trends_by_concept## Warning: Removed 5 rows containing non-finite values (stat_boxplot).
1.2 Exposure data
We have included 20 exposures in our analysis.
These exposures are based on the census tract where each mother lived at the time of enrollment into Healthy Start. With the exception of air pollution (mean_pm and mean_o3) and temperature, these are based on long-term averages at for each census tract. For the air pollutants and temerature variables, we used the average pollution levels across each pregnancy (est. conception date to delivery date) estimated using ordinary kriging and monitoring data.
#' Exposure data
X <- select(hs_data2, mean_pm, mean_o3, mean_temp, pct_tree_cover, pct_impervious,
mean_aadt_intensity, dist_m_tri:dist_m_mine_well,
cvd_rate_adj, res_rate_adj, violent_crime_rate, property_crime_rate,
pct_less_hs, pct_unemp, pct_limited_eng, pct_hh_pov, pct_poc) %>%
as.matrix()
head(X)## mean_pm mean_o3 mean_temp pct_tree_cover pct_impervious
## [1,] 8.483046 47.19072 51.81487 6.006276 43.30893
## [2,] 6.598608 50.05090 58.32885 7.281109 48.36432
## [3,] 7.454146 48.57052 58.01924 17.205991 31.67281
## [4,] 6.671239 50.06429 61.35590 6.842898 45.00359
## [5,] 7.122537 50.14275 59.28421 3.357792 28.16745
## [6,] 7.637453 47.03125 55.32825 10.743612 45.87564
## mean_aadt_intensity dist_m_tri dist_m_npl dist_m_waste_site
## [1,] 10128.4962 2827.538 729.2371 4829.780
## [2,] 10749.0359 1576.420 5239.2211 4417.792
## [3,] 9048.6468 3350.303 2992.2968 5211.871
## [4,] 4223.3434 3364.954 6998.1286 8921.318
## [5,] 858.7283 2923.811 3427.2247 7006.042
## [6,] 15603.9800 3364.200 3166.5395 4484.960
## dist_m_major_emit dist_m_cafo dist_m_mine_well cvd_rate_adj res_rate_adj
## [1,] 7968.654 29116.58 1749.1256 275.2480 155.7767
## [2,] 3780.951 51044.30 7354.5310 279.6435 226.8038
## [3,] 7423.232 36079.21 4887.2996 221.0414 157.6974
## [4,] 9636.816 42235.78 3752.6399 203.8812 142.5368
## [5,] 6806.912 29145.98 729.7784 194.1983 101.0046
## [6,] 5265.285 43921.85 5870.6867 174.3361 120.3281
## violent_crime_rate property_crime_rate pct_less_hs pct_unemp
## [1,] 14.377133 37.32935 31.784946 11.529628
## [2,] 8.905404 67.03932 15.290231 4.908306
## [3,] 7.636888 46.78194 6.891702 4.564963
## [4,] 2.850212 21.95270 2.725915 5.623583
## [5,] 5.435988 22.49834 12.919186 5.234103
## [6,] 5.035971 47.15500 3.842365 10.000000
## pct_limited_eng pct_hh_pov pct_poc
## [1,] 26.114650 12.010919 90.33703
## [2,] 8.500401 18.123496 30.44025
## [3,] 0.000000 6.307978 26.63305
## [4,] 1.350621 9.292274 32.68648
## [5,] 6.307385 2.115768 73.60772
## [6,] 5.121799 25.171768 23.08698Variance and histograms of the exposure variables (in their original units):
var(X)## mean_pm mean_o3 mean_temp pct_tree_cover
## mean_pm 0.391784015 0.006083605 0.09741867 -0.2054297
## mean_o3 0.006083605 9.383489039 11.72688428 -0.4158151
## mean_temp 0.097418667 11.726884276 20.59970005 0.4425544
## pct_tree_cover -0.205429726 -0.415815089 0.44255440 9.7193077
## pct_impervious 0.508898445 -1.674151031 3.35723856 5.8719893
## mean_aadt_intensity -182.234953786 474.627052967 2674.12174077 8431.6446632
## dist_m_tri -255.176839682 444.286548683 -627.63132786 -73.1423054
## dist_m_npl -289.002141382 539.849185829 -165.00509261 434.4654007
## dist_m_waste_site -275.262105884 261.902915064 58.19389166 1933.8647304
## dist_m_major_emit 71.096593638 577.257325397 138.98687089 265.4284518
## dist_m_cafo -1291.237441927 -35.275020052 237.89751842 10170.6234275
## dist_m_mine_well -339.250592215 -375.434990683 -202.34883778 3136.3680766
## cvd_rate_adj 3.871688575 0.939328342 7.31791796 -24.8232924
## res_rate_adj 2.356328835 -0.181515705 7.98167422 -3.5331376
## violent_crime_rate 0.232839920 0.577648302 1.07794996 -4.0583754
## property_crime_rate 2.001989749 -2.773092354 6.06649992 -22.6429724
## pct_less_hs 1.132232861 0.637361326 0.69410116 -7.5753471
## pct_unemp 0.100439902 0.288530482 0.25729682 -0.3330523
## pct_limited_eng 0.432516169 0.295617023 0.05811301 -2.8349116
## pct_hh_pov 0.731824476 -0.606648513 0.73475917 0.3805472
## pct_poc 1.632059580 1.202932299 -0.90133106 -19.4091792
## pct_impervious mean_aadt_intensity dist_m_tri
## mean_pm 0.5088984 -182.2350 -255.17684
## mean_o3 -1.6741510 474.6271 444.28655
## mean_temp 3.3572386 2674.1217 -627.63133
## pct_tree_cover 5.8719893 8431.6447 -73.14231
## pct_impervious 176.8316214 55459.6063 -15279.44024
## mean_aadt_intensity 55459.6063235 67283287.0201 -1315386.69307
## dist_m_tri -15279.4402428 -1315386.6931 6558190.20296
## dist_m_npl -7729.3843793 1683196.0799 4282727.94125
## dist_m_waste_site -4662.9983638 2039577.9230 2441267.84540
## dist_m_major_emit 2627.0270993 2477155.3406 1433153.16531
## dist_m_cafo 16586.9964129 15462371.9832 3431065.70215
## dist_m_mine_well 706.6674650 2073244.5987 995872.11873
## cvd_rate_adj 230.4542985 20477.4374 -49347.60273
## res_rate_adj 176.8108084 33055.3733 -31870.98664
## violent_crime_rate 26.6945028 5736.5627 -1014.08753
## property_crime_rate 118.0737725 22077.3894 -5365.69285
## pct_less_hs 56.8383947 -4056.6889 -12372.14262
## pct_unemp 25.9434246 6003.3343 -2527.22451
## pct_limited_eng 41.9919053 2620.6198 -5408.86434
## pct_hh_pov 82.2198624 17850.1649 -8842.76408
## pct_poc 88.3560154 4526.2710 -18049.42332
## dist_m_npl dist_m_waste_site dist_m_major_emit
## mean_pm -289.0021 -275.26211 71.09659
## mean_o3 539.8492 261.90292 577.25733
## mean_temp -165.0051 58.19389 138.98687
## pct_tree_cover 434.4654 1933.86473 265.42845
## pct_impervious -7729.3844 -4662.99836 2627.02710
## mean_aadt_intensity 1683196.0799 2039577.92299 2477155.34057
## dist_m_tri 4282727.9413 2441267.84540 1433153.16531
## dist_m_npl 11125411.7474 4193498.05859 6948817.25739
## dist_m_waste_site 4193498.0586 5344101.75397 1395277.06805
## dist_m_major_emit 6948817.2574 1395277.06805 10114549.72263
## dist_m_cafo 5416531.1320 5586018.82514 -2993791.05377
## dist_m_mine_well 256924.3029 1375784.78556 -1810174.74785
## cvd_rate_adj -30921.0390 -43119.57852 16272.40152
## res_rate_adj -19393.1304 -32402.84395 -1320.21297
## violent_crime_rate -672.9264 -3702.61118 -360.49700
## property_crime_rate -18283.4264 -22350.30055 -24007.42305
## pct_less_hs -6760.5337 -11422.49855 8866.74917
## pct_unemp 2195.0515 -1476.40942 5212.74830
## pct_limited_eng 498.0033 -4277.81339 9367.28435
## pct_hh_pov -1135.3843 -7599.74324 8682.26135
## pct_poc -1456.8941 -8602.85207 22698.24353
## dist_m_cafo dist_m_mine_well cvd_rate_adj
## mean_pm -1291.23744 -339.2506 3.8716886
## mean_o3 -35.27502 -375.4350 0.9393283
## mean_temp 237.89752 -202.3488 7.3179180
## pct_tree_cover 10170.62343 3136.3681 -24.8232924
## pct_impervious 16586.99641 706.6675 230.4542985
## mean_aadt_intensity 15462371.98316 2073244.5987 20477.4373759
## dist_m_tri 3431065.70215 995872.1187 -49347.6027339
## dist_m_npl 5416531.13199 256924.3029 -30921.0389720
## dist_m_waste_site 5586018.82514 1375784.7856 -43119.5785165
## dist_m_major_emit -2993791.05377 -1810174.7478 16272.4015197
## dist_m_cafo 46324000.89481 9345575.3772 -46645.9665229
## dist_m_mine_well 9345575.37722 4430024.9964 -39046.5984701
## cvd_rate_adj -46645.96652 -39046.5985 2039.8569530
## res_rate_adj -13772.40263 -16322.5110 1289.5661935
## violent_crime_rate 722.31907 -2032.3464 135.9487143
## property_crime_rate -15833.92381 -4272.3829 343.9364726
## pct_less_hs -26060.83378 -10037.6577 328.3044447
## pct_unemp -1030.96916 -2827.2369 105.0153846
## pct_limited_eng -7089.15821 -4814.6687 183.5853966
## pct_hh_pov -855.38016 -5030.4055 266.1004715
## pct_poc -44526.37107 -24974.3303 618.2817294
## res_rate_adj violent_crime_rate property_crime_rate
## mean_pm 2.3563288 0.2328399 2.001990
## mean_o3 -0.1815157 0.5776483 -2.773092
## mean_temp 7.9816742 1.0779500 6.066500
## pct_tree_cover -3.5331376 -4.0583754 -22.642972
## pct_impervious 176.8108084 26.6945028 118.073773
## mean_aadt_intensity 33055.3733277 5736.5627383 22077.389365
## dist_m_tri -31870.9866403 -1014.0875345 -5365.692846
## dist_m_npl -19393.1304345 -672.9263612 -18283.426420
## dist_m_waste_site -32402.8439544 -3702.6111771 -22350.300554
## dist_m_major_emit -1320.2129699 -360.4970006 -24007.423046
## dist_m_cafo -13772.4026269 722.3190727 -15833.923813
## dist_m_mine_well -16322.5110008 -2032.3464340 -4272.382880
## cvd_rate_adj 1289.5661935 135.9487143 343.936473
## res_rate_adj 1091.1856742 104.4979610 333.780710
## violent_crime_rate 104.4979610 40.1175363 160.725724
## property_crime_rate 333.7807097 160.7257236 1295.004010
## pct_less_hs 197.8827546 22.5579950 -3.138375
## pct_unemp 72.3576933 11.3130282 1.362247
## pct_limited_eng 104.0524036 12.7978322 -14.963510
## pct_hh_pov 201.6582659 29.1947400 64.236239
## pct_poc 297.8399442 46.4013012 -44.321973
## pct_less_hs pct_unemp pct_limited_eng pct_hh_pov
## mean_pm 1.1322329 0.1004399 0.43251617 0.7318245
## mean_o3 0.6373613 0.2885305 0.29561702 -0.6066485
## mean_temp 0.6941012 0.2572968 0.05811301 0.7347592
## pct_tree_cover -7.5753471 -0.3330523 -2.83491161 0.3805472
## pct_impervious 56.8383947 25.9434246 41.99190527 82.2198624
## mean_aadt_intensity -4056.6889048 6003.3343312 2620.61975287 17850.1649192
## dist_m_tri -12372.1426191 -2527.2245090 -5408.86433682 -8842.7640785
## dist_m_npl -6760.5337115 2195.0514738 498.00334199 -1135.3843390
## dist_m_waste_site -11422.4985495 -1476.4094188 -4277.81339346 -7599.7432386
## dist_m_major_emit 8866.7491706 5212.7483023 9367.28434718 8682.2613524
## dist_m_cafo -26060.8337755 -1030.9691591 -7089.15821141 -855.3801591
## dist_m_mine_well -10037.6576614 -2827.2368665 -4814.66874000 -5030.4055237
## cvd_rate_adj 328.3044447 105.0153846 183.58539661 266.1004715
## res_rate_adj 197.8827546 72.3576933 104.05240356 201.6582659
## violent_crime_rate 22.5579950 11.3130282 12.79783224 29.1947400
## property_crime_rate -3.1383751 1.3622468 -14.96351049 64.2362387
## pct_less_hs 162.1681017 39.4206217 85.19100137 100.9072175
## pct_unemp 39.4206217 24.6546969 25.21727694 36.9693212
## pct_limited_eng 85.1910014 25.2172769 68.65329426 67.2758215
## pct_hh_pov 100.9072175 36.9693212 67.27582153 119.7157808
## pct_poc 238.8801445 72.7999599 142.19618383 155.4992975
## pct_poc
## mean_pm 1.6320596
## mean_o3 1.2029323
## mean_temp -0.9013311
## pct_tree_cover -19.4091792
## pct_impervious 88.3560154
## mean_aadt_intensity 4526.2710457
## dist_m_tri -18049.4233248
## dist_m_npl -1456.8941447
## dist_m_waste_site -8602.8520680
## dist_m_major_emit 22698.2435288
## dist_m_cafo -44526.3710716
## dist_m_mine_well -24974.3303024
## cvd_rate_adj 618.2817294
## res_rate_adj 297.8399442
## violent_crime_rate 46.4013012
## property_crime_rate -44.3219731
## pct_less_hs 238.8801445
## pct_unemp 72.7999599
## pct_limited_eng 142.1961838
## pct_hh_pov 155.4992975
## pct_poc 524.7591044ggplot(pivot_longer(as.data.frame(X), mean_pm:pct_poc, names_to = "exp", values_to = "value")) +
geom_histogram(aes(x = value)) +
facet_wrap(~ exp, scales = "free")## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
Scaling the exposure variables
X.scaled <- apply(X, 2, scale)
head(X.scaled)## mean_pm mean_o3 mean_temp pct_tree_cover pct_impervious
## [1,] 1.60876944 -0.2502907 -0.1690421 -0.08261827 0.2084897
## [2,] -1.40186806 0.6834152 1.2661699 0.32629926 0.5886571
## [3,] -0.03503482 0.2001460 1.1979551 3.50981981 -0.6665506
## [4,] -1.28583023 0.6877893 1.9331141 0.18573791 0.3359288
## [5,] -0.56482237 0.7133998 1.4766616 -0.93215008 -0.9301550
## [6,] 0.25782234 -0.3023500 0.6050531 1.43693690 0.4015075
## mean_aadt_intensity dist_m_tri dist_m_npl dist_m_waste_site
## [1,] -0.02626143 -0.4008664 -1.44212141 -0.172775897
## [2,] 0.04938980 -0.8894134 -0.08999604 -0.350992130
## [3,] -0.15790801 -0.1967327 -0.76363997 -0.007492447
## [4,] -0.74617032 -0.1910117 0.43733697 1.597126043
## [5,] -1.15635722 -0.3632728 -0.63324550 0.768623456
## [6,] 0.64126566 -0.1913062 -0.71140077 -0.321936759
## dist_m_major_emit dist_m_cafo dist_m_mine_well cvd_rate_adj res_rate_adj
## [1,] -0.1090638 -1.1354079 -0.7748959 0.6917151 -0.2847192
## [2,] -1.4258114 2.0863310 1.8883051 0.7890362 1.8654606
## [3,] -0.2805619 -0.1124210 0.7160914 -0.5084805 -0.2265752
## [4,] 0.4154599 0.7921355 0.1769998 -0.8884275 -0.6855261
## [5,] -0.4743524 -1.1310891 -1.2592010 -1.1028189 -1.9428184
## [6,] -0.9590895 1.0398621 1.1833114 -1.5425892 -1.3578439
## violent_crime_rate property_crime_rate pct_less_hs pct_unemp
## [1,] 0.2444833 -0.5008789 1.20091488 0.36793456
## [2,] -0.6194047 0.3247153 -0.09436047 -0.96557105
## [3,] -0.8196807 -0.2382061 -0.75386917 -1.03471894
## [4,] -1.5754111 -0.9281724 -1.08099463 -0.82151747
## [5,] -1.1671633 -0.9130100 -0.28055077 -0.89995692
## [6,] -1.2303189 -0.2278392 -0.99332353 0.05987409
## pct_limited_eng pct_hh_pov pct_poc
## [1,] 2.15383825 -0.3020187 1.5727240
## [2,] 0.02798425 0.2566428 -1.0419857
## [3,] -0.99792447 -0.8232412 -1.2081839
## [4,] -0.83491873 -0.5504902 -0.9439299
## [5,] -0.23668961 -1.2063898 0.8424295
## [6,] -0.37977738 0.9008223 -1.3629822Variance and histograms of the exposure variables (scaled):
var(X.scaled)## mean_pm mean_o3 mean_temp pct_tree_cover
## mean_pm 1.000000000 0.003172893 0.034291650 -0.105274276
## mean_o3 0.003172893 1.000000000 0.843470729 -0.043541201
## mean_temp 0.034291650 0.843470729 1.000000000 0.031276529
## pct_tree_cover -0.105274276 -0.043541201 0.031276529 1.000000000
## pct_impervious 0.061140333 -0.041099117 0.055625226 0.141640558
## mean_aadt_intensity -0.035493982 0.018889337 0.071828554 0.329716765
## dist_m_tri -0.159193706 0.056635532 -0.053998558 -0.009161339
## dist_m_npl -0.138426634 0.052836279 -0.010899557 0.041781063
## dist_m_waste_site -0.190232937 0.036984589 0.005546380 0.268331135
## dist_m_major_emit 0.035715124 0.059253499 0.009628753 0.026770503
## dist_m_cafo -0.303095664 -0.001691929 0.007701165 0.479321466
## dist_m_mine_well -0.257510042 -0.058230361 -0.021182010 0.477976199
## cvd_rate_adj 0.136954783 0.006789463 0.035699097 -0.176295758
## res_rate_adj 0.113962827 -0.001793836 0.053237079 -0.034307854
## violent_crime_rate 0.058730941 0.029772424 0.037497389 -0.205526308
## property_crime_rate 0.088879773 -0.025156291 0.037142591 -0.201827442
## pct_less_hs 0.142046220 0.016338825 0.012009076 -0.190810449
## pct_unemp 0.032317153 0.018969666 0.011417056 -0.021515177
## pct_limited_eng 0.083396591 0.011647067 0.001545298 -0.109746623
## pct_hh_pov 0.106858205 -0.018100029 0.014795814 0.011156172
## pct_poc 0.113823690 0.017142692 -0.008669098 -0.271775006
## pct_impervious mean_aadt_intensity dist_m_tri dist_m_npl
## mean_pm 0.06114033 -0.03549398 -0.159193706 -0.13842663
## mean_o3 -0.04109912 0.01888934 0.056635532 0.05283628
## mean_temp 0.05562523 0.07182855 -0.053998558 -0.01089956
## pct_tree_cover 0.14164056 0.32971677 -0.009161339 0.04178106
## pct_impervious 1.00000000 0.50844411 -0.448678724 -0.17426369
## mean_aadt_intensity 0.50844411 1.00000000 -0.062619247 0.06152095
## dist_m_tri -0.44867872 -0.06261925 1.000000000 0.50138396
## dist_m_npl -0.17426369 0.06152095 0.501383960 1.00000000
## dist_m_waste_site -0.15168685 0.10755964 0.412369055 0.54385239
## dist_m_major_emit 0.06211712 0.09495686 0.175965418 0.65505772
## dist_m_cafo 0.18326720 0.27696155 0.196849357 0.23859436
## dist_m_mine_well 0.02524829 0.12008641 0.184760224 0.03659688
## cvd_rate_adj 0.38371166 0.05527416 -0.426652406 -0.20525615
## res_rate_adj 0.40251263 0.12199419 -0.376750794 -0.17601130
## violent_crime_rate 0.31693831 0.11041575 -0.062519618 -0.03185242
## property_crime_rate 0.24673907 0.07479259 -0.058223492 -0.15232247
## pct_less_hs 0.33564418 -0.03883608 -0.379376300 -0.15916230
## pct_unemp 0.39291400 0.14739715 -0.198747643 0.13253691
## pct_limited_eng 0.38111402 0.03855846 -0.254907958 0.01801953
## pct_hh_pov 0.56509450 0.19888999 -0.315587892 -0.03111065
## pct_poc 0.29005220 0.02408835 -0.307674381 -0.01906733
## dist_m_waste_site dist_m_major_emit dist_m_cafo
## mean_pm -0.19023294 0.035715124 -0.303095664
## mean_o3 0.03698459 0.059253499 -0.001691929
## mean_temp 0.00554638 0.009628753 0.007701165
## pct_tree_cover 0.26833114 0.026770503 0.479321466
## pct_impervious -0.15168685 0.062117120 0.183267205
## mean_aadt_intensity 0.10755964 0.094956864 0.276961553
## dist_m_tri 0.41236906 0.175965418 0.196849357
## dist_m_npl 0.54385239 0.655057717 0.238594356
## dist_m_waste_site 1.00000000 0.189779728 0.355027509
## dist_m_major_emit 0.18977973 1.000000000 -0.138307324
## dist_m_cafo 0.35502751 -0.138307324 1.000000000
## dist_m_mine_well 0.28275484 -0.270423318 0.652378929
## cvd_rate_adj -0.41298787 0.113286594 -0.151743889
## res_rate_adj -0.42432287 -0.012566704 -0.061257230
## violent_crime_rate -0.25287368 -0.017896218 0.016755559
## property_crime_rate -0.26866460 -0.209766780 -0.064647236
## pct_less_hs -0.38800832 0.218931589 -0.300678627
## pct_unemp -0.12862329 0.330098571 -0.030506530
## pct_limited_eng -0.22333346 0.355475551 -0.125707430
## pct_hh_pov -0.30045944 0.249507656 -0.011486308
## pct_poc -0.16245202 0.311558055 -0.285584268
## dist_m_mine_well cvd_rate_adj res_rate_adj
## mean_pm -0.25751004 0.136954783 0.113962827
## mean_o3 -0.05823036 0.006789463 -0.001793836
## mean_temp -0.02118201 0.035699097 0.053237079
## pct_tree_cover 0.47797620 -0.176295758 -0.034307854
## pct_impervious 0.02524829 0.383711656 0.402512635
## mean_aadt_intensity 0.12008641 0.055274160 0.121994187
## dist_m_tri 0.18476022 -0.426652406 -0.376750794
## dist_m_npl 0.03659688 -0.205256148 -0.176011297
## dist_m_waste_site 0.28275484 -0.412987865 -0.424322872
## dist_m_major_emit -0.27042332 0.113286594 -0.012566704
## dist_m_cafo 0.65237893 -0.151743889 -0.061257230
## dist_m_mine_well 1.00000000 -0.410752544 -0.234765650
## cvd_rate_adj -0.41075254 1.000000000 0.864359590
## res_rate_adj -0.23476565 0.864359590 1.000000000
## violent_crime_rate -0.15245003 0.475234675 0.499449246
## property_crime_rate -0.05640681 0.211613232 0.280786581
## pct_less_hs -0.37449548 0.570813439 0.470409304
## pct_unemp -0.27052616 0.468277441 0.441149256
## pct_limited_eng -0.27607853 0.490577454 0.380164971
## pct_hh_pov -0.21843600 0.538480631 0.557944498
## pct_poc -0.51797735 0.597594464 0.393598671
## violent_crime_rate property_crime_rate pct_less_hs
## mean_pm 0.05873094 0.088879773 0.14204622
## mean_o3 0.02977242 -0.025156291 0.01633882
## mean_temp 0.03749739 0.037142591 0.01200908
## pct_tree_cover -0.20552631 -0.201827442 -0.19081045
## pct_impervious 0.31693831 0.246739067 0.33564418
## mean_aadt_intensity 0.11041575 0.074792588 -0.03883608
## dist_m_tri -0.06251962 -0.058223492 -0.37937630
## dist_m_npl -0.03185242 -0.152322474 -0.15916230
## dist_m_waste_site -0.25287368 -0.268664603 -0.38800832
## dist_m_major_emit -0.01789622 -0.209766780 0.21893159
## dist_m_cafo 0.01675556 -0.064647236 -0.30067863
## dist_m_mine_well -0.15245003 -0.056406808 -0.37449548
## cvd_rate_adj 0.47523468 0.211613232 0.57081344
## res_rate_adj 0.49944925 0.280786581 0.47040930
## violent_crime_rate 1.00000000 0.705151942 0.27967307
## property_crime_rate 0.70515194 1.000000000 -0.00684836
## pct_less_hs 0.27967307 -0.006848360 1.00000000
## pct_unemp 0.35971778 0.007623781 0.62343462
## pct_limited_eng 0.24385889 -0.050184228 0.80738433
## pct_hh_pov 0.42127121 0.163143151 0.72420883
## pct_poc 0.31980337 -0.053765481 0.81887450
## pct_unemp pct_limited_eng pct_hh_pov pct_poc
## mean_pm 0.032317153 0.083396591 0.10685820 0.113823690
## mean_o3 0.018969666 0.011647067 -0.01810003 0.017142692
## mean_temp 0.011417056 0.001545298 0.01479581 -0.008669098
## pct_tree_cover -0.021515177 -0.109746623 0.01115617 -0.271775006
## pct_impervious 0.392914001 0.381114020 0.56509450 0.290052202
## mean_aadt_intensity 0.147397153 0.038558463 0.19888999 0.024088345
## dist_m_tri -0.198747643 -0.254907958 -0.31558789 -0.307674381
## dist_m_npl 0.132536906 0.018019533 -0.03111065 -0.019067333
## dist_m_waste_site -0.128623290 -0.223333456 -0.30045944 -0.162452016
## dist_m_major_emit 0.330098571 0.355475551 0.24950766 0.311558055
## dist_m_cafo -0.030506530 -0.125707430 -0.01148631 -0.285584268
## dist_m_mine_well -0.270526163 -0.276078529 -0.21843600 -0.517977353
## cvd_rate_adj 0.468277441 0.490577454 0.53848063 0.597594464
## res_rate_adj 0.441149256 0.380164971 0.55794450 0.393598671
## violent_crime_rate 0.359717785 0.243858891 0.42127121 0.319803374
## property_crime_rate 0.007623781 -0.050184228 0.16314315 -0.053765481
## pct_less_hs 0.623434625 0.807384330 0.72420883 0.818874497
## pct_unemp 1.000000000 0.612939575 0.68048090 0.640031449
## pct_limited_eng 0.612939575 1.000000000 0.74208323 0.749164620
## pct_hh_pov 0.680480902 0.742083231 1.00000000 0.620401357
## pct_poc 0.640031449 0.749164620 0.62040136 1.000000000ggplot(pivot_longer(as.data.frame(X.scaled), mean_pm:pct_poc,
names_to = "exp", values_to = "value")) +
geom_histogram(aes(x = value)) +
facet_wrap(~ exp, scales = "free")## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
1.3 Covariate data
Covariates were assessed at the individual level. These were selected based on previous HS studies and others in the literature and informed by a DAG.
W <- select(hs_data2,
lat, lon, lat_lon_int,
latina_re, black_re, other_re,
ed_no_hs, ed_hs, ed_aa, ed_4yr,
low_bmi, ovwt_bmi, obese_bmi,
concep_spring, concep_summer, concep_fall,
concep_2010, concep_2011, concep_2012, concep_2013,
maternal_age, any_smoker, smokeSH, mean_cpss, mean_epsd,
male, gest_age_w) %>%
as.matrix()
head(W)## lat lon lat_lon_int latina_re black_re other_re ed_no_hs ed_hs
## [1,] 39.79402 -104.8133 -4170.944 1 0 0 0 0
## [2,] 39.62671 -104.9927 -4160.517 0 0 1 0 0
## [3,] 39.74934 -104.9129 -4170.219 0 0 0 0 0
## [4,] 39.68397 -104.8933 -4162.583 0 0 0 0 0
## [5,] 39.79134 -104.7669 -4168.814 0 1 0 0 0
## [6,] 39.68050 -104.9451 -4164.274 1 0 0 0 0
## ed_aa ed_4yr low_bmi ovwt_bmi obese_bmi concep_spring concep_summer
## [1,] 1 0 0 0 0 0 0
## [2,] 1 0 0 0 0 0 0
## [3,] 0 0 0 0 0 0 0
## [4,] 1 0 0 0 0 1 0
## [5,] 0 1 0 0 0 1 0
## [6,] 1 0 0 0 0 0 0
## concep_fall concep_2010 concep_2011 concep_2012 concep_2013 maternal_age
## [1,] 0 0 0 0 0 19
## [2,] 0 1 0 0 0 36
## [3,] 0 1 0 0 0 34
## [4,] 0 1 0 0 0 28
## [5,] 0 1 0 0 0 30
## [6,] 0 1 0 0 0 22
## any_smoker smokeSH mean_cpss mean_epsd male gest_age_w
## [1,] 0 1 29 0 0 40.57143
## [2,] 0 0 19 2 1 35.85714
## [3,] 0 0 19 1 0 40.42857
## [4,] 0 0 20 0 0 36.28571
## [5,] 0 0 15 0 1 38.42857
## [6,] 0 0 17 1 0 40.71429Scaled the non-binary (continuous) covariates
colnames(W)## [1] "lat" "lon" "lat_lon_int" "latina_re"
## [5] "black_re" "other_re" "ed_no_hs" "ed_hs"
## [9] "ed_aa" "ed_4yr" "low_bmi" "ovwt_bmi"
## [13] "obese_bmi" "concep_spring" "concep_summer" "concep_fall"
## [17] "concep_2010" "concep_2011" "concep_2012" "concep_2013"
## [21] "maternal_age" "any_smoker" "smokeSH" "mean_cpss"
## [25] "mean_epsd" "male" "gest_age_w"W.s <- apply(W[,c(1, 2, 3, 21, 24, 25, 27)], 2, scale) #' just the continuous ones
W.scaled <- cbind(W.s[,1:3],
W[,4:20], W.s[,4],
W[,22:23], W.s[,5:6],
W[,26], W.s[,7])
colnames(W.scaled)## [1] "lat" "lon" "lat_lon_int" "latina_re"
## [5] "black_re" "other_re" "ed_no_hs" "ed_hs"
## [9] "ed_aa" "ed_4yr" "low_bmi" "ovwt_bmi"
## [13] "obese_bmi" "concep_spring" "concep_summer" "concep_fall"
## [17] "concep_2010" "concep_2011" "concep_2012" "concep_2013"
## [21] "" "any_smoker" "smokeSH" "mean_cpss"
## [25] "mean_epsd" "" ""colnames(W.scaled) <- colnames(W)
head(W.scaled)## lat lon lat_lon_int latina_re black_re other_re ed_no_hs
## [1,] 0.9587536 0.5410850 -0.5821980 1 0 0 0
## [2,] -1.5498523 -1.6236392 0.6519093 0 0 1 0
## [3,] 0.2887793 -0.6606299 -0.4964164 0 0 0 0
## [4,] -0.6913627 -0.4239607 0.4073829 0 0 0 0
## [5,] 0.9185421 1.1019032 -0.3300513 0 1 0 0
## [6,] -0.7433125 -1.0489343 0.2071583 1 0 0 0
## ed_hs ed_aa ed_4yr low_bmi ovwt_bmi obese_bmi concep_spring concep_summer
## [1,] 0 1 0 0 0 0 0 0
## [2,] 0 1 0 0 0 0 0 0
## [3,] 0 0 0 0 0 0 0 0
## [4,] 0 1 0 0 0 0 1 0
## [5,] 0 0 1 0 0 0 1 0
## [6,] 0 1 0 0 0 0 0 0
## concep_fall concep_2010 concep_2011 concep_2012 concep_2013 maternal_age
## [1,] 0 0 0 0 0 -1.39815187
## [2,] 0 1 0 0 0 1.35109608
## [3,] 0 1 0 0 0 1.02765515
## [4,] 0 1 0 0 0 0.05733234
## [5,] 0 1 0 0 0 0.38077328
## [6,] 0 1 0 0 0 -0.91299047
## any_smoker smokeSH mean_cpss mean_epsd male gest_age_w
## [1,] 0 1 3.3147856 -1.2832098 0 0.7037686
## [2,] 0 0 0.1179652 -0.6860171 1 -1.9146645
## [3,] 0 0 0.1179652 -0.9846134 0 0.6244221
## [4,] 0 0 0.4376472 -1.2832098 0 -1.6766251
## [5,] 0 0 -1.1607630 -1.2832098 1 -0.4864283
## [6,] 0 0 -0.5213989 -0.9846134 0 0.7831150summary(W.scaled)## lat lon lat_lon_int latina_re
## Min. :-2.45418 Min. :-2.5043 Min. :-3.48430 Min. :0.0000
## 1st Qu.:-0.62577 1st Qu.:-0.5848 1st Qu.:-0.48738 1st Qu.:0.0000
## Median : 0.03151 Median : 0.1214 Median : 0.02121 Median :0.0000
## Mean : 0.00000 Mean : 0.0000 Mean : 0.00000 Mean :0.2653
## 3rd Qu.: 0.42402 3rd Qu.: 0.6654 3rd Qu.: 0.60627 3rd Qu.:1.0000
## Max. : 4.00304 Max. : 4.5531 Max. : 2.60273 Max. :1.0000
## black_re other_re ed_no_hs ed_hs
## Min. :0.0000 Min. :0.00000 Min. :0.0000 Min. :0.0000
## 1st Qu.:0.0000 1st Qu.:0.00000 1st Qu.:0.0000 1st Qu.:0.0000
## Median :0.0000 Median :0.00000 Median :0.0000 Median :0.0000
## Mean :0.1717 Mean :0.06689 Mean :0.1527 Mean :0.1851
## 3rd Qu.:0.0000 3rd Qu.:0.00000 3rd Qu.:0.0000 3rd Qu.:0.0000
## Max. :1.0000 Max. :1.00000 Max. :1.0000 Max. :1.0000
## ed_aa ed_4yr low_bmi ovwt_bmi
## Min. :0.0000 Min. :0.0000 Min. :0.00000 Min. :0.000
## 1st Qu.:0.0000 1st Qu.:0.0000 1st Qu.:0.00000 1st Qu.:0.000
## Median :0.0000 Median :0.0000 Median :0.00000 Median :0.000
## Mean :0.2319 Mean :0.2185 Mean :0.03344 Mean :0.262
## 3rd Qu.:0.0000 3rd Qu.:0.0000 3rd Qu.:0.00000 3rd Qu.:1.000
## Max. :1.0000 Max. :1.0000 Max. :1.00000 Max. :1.000
## obese_bmi concep_spring concep_summer concep_fall
## Min. :0.0000 Min. :0.0000 Min. :0.0000 Min. :0.0000
## 1st Qu.:0.0000 1st Qu.:0.0000 1st Qu.:0.0000 1st Qu.:0.0000
## Median :0.0000 Median :0.0000 Median :0.0000 Median :0.0000
## Mean :0.1996 Mean :0.2497 Mean :0.2408 Mean :0.2709
## 3rd Qu.:0.0000 3rd Qu.:0.0000 3rd Qu.:0.0000 3rd Qu.:1.0000
## Max. :1.0000 Max. :1.0000 Max. :1.0000 Max. :1.0000
## concep_2010 concep_2011 concep_2012 concep_2013
## Min. :0.0000 Min. :0.0000 Min. :0.0000 Min. :0.0000
## 1st Qu.:0.0000 1st Qu.:0.0000 1st Qu.:0.0000 1st Qu.:0.0000
## Median :0.0000 Median :0.0000 Median :0.0000 Median :0.0000
## Mean :0.1616 Mean :0.3021 Mean :0.2932 Mean :0.2419
## 3rd Qu.:0.0000 3rd Qu.:1.0000 3rd Qu.:1.0000 3rd Qu.:0.0000
## Max. :1.0000 Max. :1.0000 Max. :1.0000 Max. :1.0000
## maternal_age any_smoker smokeSH mean_cpss
## Min. :-1.88331 Min. :0.00000 Min. :0.0000 Min. :-5.9560
## 1st Qu.:-0.91299 1st Qu.:0.00000 1st Qu.:0.0000 1st Qu.:-0.5214
## Median : 0.05733 Median :0.00000 Median :0.0000 Median : 0.0114
## Mean : 0.00000 Mean :0.08696 Mean :0.2575 Mean : 0.0000
## 3rd Qu.: 0.70421 3rd Qu.:0.00000 3rd Qu.:1.0000 3rd Qu.: 0.5442
## Max. : 2.64486 Max. :1.00000 Max. :1.0000 Max. : 4.5935
## mean_epsd male gest_age_w
## Min. :-1.2832 Min. :0.0000 Min. :-7.7070
## 1st Qu.:-0.7855 1st Qu.:0.0000 1st Qu.:-0.3277
## Median :-0.1884 Median :1.0000 Median : 0.1483
## Mean : 0.0000 Mean :0.5117 Mean : 0.0000
## 3rd Qu.: 0.6079 3rd Qu.:1.0000 3rd Qu.: 0.6244
## Max. : 6.0324 Max. :1.0000 Max. : 2.9255Variance and histograms for the scaled covariates
var(W.scaled)## lat lon lat_lon_int latina_re
## lat 1.0000000000 -0.25261855699 -0.9261702843 0.02075377736
## lon -0.2526185570 1.00000000000 0.5988415501 0.01061991294
## lat_lon_int -0.9261702843 0.59884155012 1.0000000000 -0.01302007756
## latina_re 0.0207537774 0.01061991294 -0.0130200776 0.19514701784
## black_re -0.0122649034 0.04784916212 0.0288174353 -0.04560340022
## other_re -0.0009403195 -0.00123694771 0.0002902002 -0.01776755853
## ed_no_hs 0.0058668471 0.01732912905 0.0019047436 0.03978788422
## ed_hs -0.0130652792 0.04117136599 0.0268694085 0.02896808807
## ed_aa -0.0071789427 0.04676104709 0.0241824221 0.01318258282
## ed_4yr 0.0022352364 -0.00766878563 -0.0048607788 -0.03571926262
## low_bmi -0.0029774584 -0.00003551643 0.0024531145 0.00004479216
## ovwt_bmi 0.0205880066 0.00512460048 -0.0150602639 0.02081218148
## obese_bmi 0.0165669344 0.00976713009 -0.0098964732 0.02065416468
## concep_spring 0.0143292896 -0.00046075172 -0.0120393632 -0.00606436136
## concep_summer -0.0140319053 -0.00711327850 0.0088444045 -0.00481142499
## concep_fall 0.0054905592 0.01642183233 0.0018457750 0.01732710225
## concep_2010 0.0110681241 0.00844610317 -0.0058861055 -0.00610790930
## concep_2011 -0.0220635440 0.01869831001 0.0255410960 -0.00882156792
## concep_2012 0.0024435961 -0.00706763788 -0.0047707939 0.01252065416
## concep_2013 0.0074817863 -0.02068066481 -0.0142344221 0.00158887761
## maternal_age 0.0307789398 -0.17980907079 -0.0955945618 -0.10858833047
## any_smoker -0.0082274331 0.02279799333 0.0156963705 -0.00858889752
## smokeSH -0.0111042258 0.04668855425 0.0273846128 -0.00590510033
## mean_cpss -0.0258360855 -0.01114736129 0.0170462313 -0.04668314421
## mean_epsd -0.0347375477 0.05084465609 0.0485855489 0.04322362524
## male 0.0290047629 -0.02552947737 -0.0339519192 -0.00087717989
## gest_age_w 0.0111191604 -0.03926647196 -0.0245324539 -0.02639363168
## black_re other_re ed_no_hs ed_hs
## lat -0.0122649034 -0.0009403195 0.0058668471 -0.01306527915
## lon 0.0478491621 -0.0012369477 0.0173291290 0.04117136599
## lat_lon_int 0.0288174353 0.0002902002 0.0019047436 0.02686940852
## latina_re -0.0456034002 -0.0177675585 0.0397878842 0.02896808807
## black_re 0.1423669175 -0.0114966555 0.0128118032 0.01506758640
## other_re -0.0114966555 0.0624850693 -0.0035311156 0.00658071548
## ed_no_hs 0.0128118032 -0.0035311156 0.1295488931 -0.02829620561
## ed_hs 0.0150675864 0.0065807155 -0.0282962056 0.15098194378
## ed_aa 0.0192967133 0.0023291925 -0.0354554865 -0.04296066253
## ed_4yr -0.0163503842 -0.0034713927 -0.0334099777 -0.04048216276
## low_bmi 0.0020641722 -0.0011235368 -0.0039977007 -0.00173196369
## ovwt_bmi -0.0003857103 -0.0052668120 0.0045849757 -0.00612657270
## obese_bmi 0.0069962872 0.0022620043 0.0063181836 0.02441297380
## concep_spring 0.0017220099 0.0044829491 -0.0002364031 0.00395788541
## concep_summer -0.0079058170 0.0017319637 -0.0044530877 -0.00331835284
## concep_fall -0.0063828834 -0.0047479694 0.0110338032 0.00226573698
## concep_2010 0.0090467730 -0.0007801302 -0.0001629937 0.00576574693
## concep_2011 0.0183859392 -0.0023739847 0.0096091635 -0.00463350056
## concep_2012 -0.0146793876 0.0004553870 -0.0035360925 0.00371526119
## concep_2013 -0.0125617136 0.0027733815 -0.0057396182 -0.00464096592
## maternal_age -0.0895968722 -0.0133074822 -0.1376124653 -0.10868310364
## any_smoker 0.0185364907 -0.0013586957 0.0179541925 0.00174689441
## smokeSH 0.0349789477 0.0084246596 0.0309364548 0.02483352246
## mean_cpss -0.0233123370 0.0255604593 -0.0561153540 -0.03433895561
## mean_epsd 0.0220578552 0.0202679881 0.0670107276 0.02014619096
## male 0.0002202281 0.0003322086 -0.0135085702 0.00006345557
## gest_age_w -0.0368471269 -0.0054750903 -0.0076928484 -0.01723767893
## ed_aa ed_4yr low_bmi ovwt_bmi
## lat -0.007178943 0.0022352364 -0.00297745845 0.0205880066
## lon 0.046761047 -0.0076687856 -0.00003551643 0.0051246005
## lat_lon_int 0.024182422 -0.0048607788 0.00245311454 -0.0150602639
## latina_re 0.013182583 -0.0357192626 0.00004479216 0.0208121815
## black_re 0.019296713 -0.0163503842 0.00206417224 -0.0003857103
## other_re 0.002329193 -0.0034713927 -0.00112353679 -0.0052668120
## ed_no_hs -0.035455487 -0.0334099777 -0.00399770067 0.0045849757
## ed_hs -0.042960663 -0.0404821628 -0.00173196369 -0.0061265727
## ed_aa 0.178312629 -0.0507246377 0.00786102484 0.0150750518
## ed_4yr -0.050724638 0.1709517837 -0.00173569637 0.0040748427
## low_bmi 0.007861025 -0.0017356964 0.03236233875 -0.0087717989
## ovwt_bmi 0.015075052 0.0040748427 -0.00877179885 0.1935643614
## obese_bmi 0.009478520 -0.0124024526 -0.00668149785 -0.0523383998
## concep_spring 0.006761128 -0.0066354615 -0.00501298973 0.0092806876
## concep_summer -0.011257764 0.0064762004 0.00309812470 -0.0051212375
## concep_fall -0.007084627 0.0010078237 0.00320637243 0.0026091436
## concep_2010 0.004884834 0.0003533604 0.00128404204 -0.0033345278
## concep_2011 0.002410067 0.0053402214 0.00439336479 0.0055828456
## concep_2012 -0.005564182 -0.0061016882 -0.00535266364 -0.0043547938
## concep_2013 -0.002587992 0.0006519748 -0.00028741639 0.0023988692
## maternal_age -0.040296710 0.1091044519 -0.01089529356 0.0089002276
## any_smoker 0.011063665 -0.0156735248 0.00155279503 -0.0060656056
## smokeSH 0.022806677 -0.0362443263 0.00142215122 -0.0106232083
## mean_cpss 0.030714793 0.0282429323 0.00484169668 -0.0082476896
## mean_epsd 0.025424770 -0.0463684315 0.00946748435 -0.0019127169
## male 0.000630823 0.0063679527 -0.00262407430 0.0008361204
## gest_age_w -0.035168407 0.0301476493 -0.00601412877 -0.0148466585
## obese_bmi concep_spring concep_summer concep_fall
## lat 0.0165669344 0.0143292896 -0.01403190526 0.0054905592
## lon 0.0097671301 -0.0004607517 -0.00711327850 0.0164218323
## lat_lon_int -0.0098964732 -0.0120393632 0.00884440451 0.0018457750
## latina_re 0.0206541647 -0.0060643614 -0.00481142499 0.0173271022
## black_re 0.0069962872 0.0017220099 -0.00790581701 -0.0063828834
## other_re 0.0022620043 0.0044829491 0.00173196369 -0.0047479694
## ed_no_hs 0.0063181836 -0.0002364031 -0.00445308767 0.0110338032
## ed_hs 0.0244129738 0.0039578854 -0.00331835284 0.0022657370
## ed_aa 0.0094785197 0.0067611284 -0.01125776398 -0.0070846273
## ed_4yr -0.0124024526 -0.0066354615 0.00647620043 0.0010078237
## low_bmi -0.0066814978 -0.0050129897 0.00309812470 0.0032063724
## ovwt_bmi -0.0523383998 0.0092806876 -0.00512123746 0.0026091436
## obese_bmi 0.1599105152 -0.0085938744 -0.00346392738 0.0005673674
## concep_spring -0.0085938744 0.1875696767 -0.06020066890 -0.0677257525
## concep_summer -0.0034639274 -0.0602006689 0.18302078356 -0.0653069756
## concep_fall 0.0005673674 -0.0677257525 -0.06530697563 0.1977350096
## concep_2010 -0.0043921206 -0.0236714146 0.00009331701 0.0287043120
## concep_2011 0.0032598742 0.0003633142 -0.00140348782 -0.0127396381
## concep_2012 0.0072737498 -0.0085677457 0.00186260750 0.0019559245
## concep_2013 -0.0059187868 0.0321545529 -0.00028368371 -0.0176182513
## maternal_age 0.0027900741 -0.0149065532 0.01490413862 -0.0196470231
## any_smoker 0.0027173913 0.0016983696 0.00024262422 -0.0023777174
## smokeSH 0.0110524666 -0.0041134138 -0.00627836837 -0.0028778966
## mean_cpss -0.0087226114 0.0079650833 0.01166899615 -0.0055888831
## mean_epsd 0.0281330380 -0.0063209443 -0.01563660013 0.0265650931
## male -0.0017804885 -0.0062746357 -0.00393797778 0.0018476768
## gest_age_w -0.0214614301 -0.0179961830 0.01920131892 0.0141959621
## concep_2010 concep_2011 concep_2012 concep_2013
## lat 0.01106812411 -0.0220635440 0.002443596 0.0074817863
## lon 0.00844610317 0.0186983100 -0.007067638 -0.0206806648
## lat_lon_int -0.00588610547 0.0255410960 -0.004770794 -0.0142344221
## latina_re -0.00610790930 -0.0088215679 0.012520654 0.0015888776
## black_re 0.00904677297 0.0183859392 -0.014679388 -0.0125617136
## other_re -0.00078013020 -0.0023739847 0.000455387 0.0027733815
## ed_no_hs -0.00016299371 0.0096091635 -0.003536093 -0.0057396182
## ed_hs 0.00576574693 -0.0046335006 0.003715261 -0.0046409659
## ed_aa 0.00488483437 0.0024100673 -0.005564182 -0.0025879917
## ed_4yr 0.00035336041 0.0053402214 -0.006101688 0.0006519748
## low_bmi 0.00128404204 0.0043933648 -0.005352664 -0.0002874164
## ovwt_bmi -0.00333452779 0.0055828456 -0.004354794 0.0023988692
## obese_bmi -0.00439212056 0.0032598742 0.007273750 -0.0059187868
## concep_spring -0.02367141464 0.0003633142 -0.008567746 0.0321545529
## concep_summer 0.00009331701 -0.0014034878 0.001862608 -0.0002836837
## concep_fall 0.02870431199 -0.0127396381 0.001955925 -0.0176182513
## concep_2010 0.13567048893 -0.0488918916 -0.047448589 -0.0391495959
## concep_2011 -0.04889189162 0.2110780976 -0.088679776 -0.0731692447
## concep_2012 -0.04744858855 -0.0886797758 0.207464863 -0.0710092670
## concep_2013 -0.03914959588 -0.0731692447 -0.071009267 0.1835981048
## maternal_age -0.02663971411 -0.0380704459 0.031448396 0.0348222009
## any_smoker 0.00266886646 0.0105298913 -0.011015140 -0.0020865683
## smokeSH 0.00631569517 0.0136280160 -0.018670867 -0.0021014990
## mean_cpss 0.00832724099 -0.0113573536 -0.011161856 0.0104924310
## mean_epsd -0.01748485806 0.0347867417 -0.022850868 0.0069811381
## male 0.00089584329 -0.0029824116 -0.001761825 0.0044194935
## gest_age_w 0.01072301448 -0.0118973482 -0.026416733 0.0268056111
## maternal_age any_smoker smokeSH mean_cpss mean_epsd
## lat 0.030778940 -0.0082274331 -0.011104226 -0.025836085 -0.034737548
## lon -0.179809071 0.0227979933 0.046688554 -0.011147361 0.050844656
## lat_lon_int -0.095594562 0.0156963705 0.027384613 0.017046231 0.048585549
## latina_re -0.108588330 -0.0085888975 -0.005905100 -0.046683144 0.043223625
## black_re -0.089596872 0.0185364907 0.034978948 -0.023312337 0.022057855
## other_re -0.013307482 -0.0013586957 0.008424660 0.025560459 0.020267988
## ed_no_hs -0.137612465 0.0179541925 0.030936455 -0.056115354 0.067010728
## ed_hs -0.108683104 0.0017468944 0.024833522 -0.034338956 0.020146191
## ed_aa -0.040296710 0.0110636646 0.022806677 0.030714793 0.025424770
## ed_4yr 0.109104452 -0.0156735248 -0.036244326 0.028242932 -0.046368432
## low_bmi -0.010895294 0.0015527950 0.001422151 0.004841697 0.009467484
## ovwt_bmi 0.008900228 -0.0060656056 -0.010623208 -0.008247690 -0.001912717
## obese_bmi 0.002790074 0.0027173913 0.011052467 -0.008722611 0.028133038
## concep_spring -0.014906553 0.0016983696 -0.004113414 0.007965083 -0.006320944
## concep_summer 0.014904139 0.0002426242 -0.006278368 0.011668996 -0.015636600
## concep_fall -0.019647023 -0.0023777174 -0.002877897 -0.005588883 0.026565093
## concep_2010 -0.026639714 0.0026688665 0.006315695 0.008327241 -0.017484858
## concep_2011 -0.038070446 0.0105298913 0.013628016 -0.011357354 0.034786742
## concep_2012 0.031448396 -0.0110151398 -0.018670867 -0.011161856 -0.022850868
## concep_2013 0.034822201 -0.0020865683 -0.002101499 0.010492431 0.006981138
## maternal_age 1.000000000 -0.0466296108 -0.155964054 0.100637638 -0.160410684
## any_smoker -0.046629611 0.0794836957 0.049010093 0.017642908 0.042144665
## smokeSH -0.155964054 0.0490100932 0.191419314 0.031721118 0.108180210
## mean_cpss 0.100637638 0.0176429080 0.031721118 1.000000000 0.455187203
## mean_epsd -0.160410684 0.0421446647 0.108180210 0.455187203 1.000000000
## male 0.023413804 0.0023291925 0.002004449 -0.003315304 0.001541815
## gest_age_w 0.091663607 -0.0149814181 -0.050311537 -0.037142336 -0.137187808
## male gest_age_w
## lat 0.02900476291 0.011119160
## lon -0.02552947737 -0.039266472
## lat_lon_int -0.03395191918 -0.024532454
## latina_re -0.00087717989 -0.026393632
## black_re 0.00022022814 -0.036847127
## other_re 0.00033220855 -0.005475090
## ed_no_hs -0.01350857023 -0.007692848
## ed_hs 0.00006345557 -0.017237679
## ed_aa 0.00063082298 -0.035168407
## ed_4yr 0.00636795270 0.030147649
## low_bmi -0.00262407430 -0.006014129
## ovwt_bmi 0.00083612040 -0.014846658
## obese_bmi -0.00178048853 -0.021461430
## concep_spring -0.00627463569 -0.017996183
## concep_summer -0.00393797778 0.019201319
## concep_fall 0.00184767678 0.014195962
## concep_2010 0.00089584329 0.010723014
## concep_2011 -0.00298241161 -0.011897348
## concep_2012 -0.00176182513 -0.026416733
## concep_2013 0.00441949355 0.026805611
## maternal_age 0.02341380415 0.091663607
## any_smoker 0.00232919255 -0.014981418
## smokeSH 0.00200444935 -0.050311537
## mean_cpss -0.00331530432 -0.037142336
## mean_epsd 0.00154181454 -0.137187808
## male 0.25014184185 -0.007427180
## gest_age_w -0.00742717951 1.000000000ggplot(pivot_longer(as.data.frame(W.scaled), lat:gest_age_w,
names_to = "exp", values_to = "value")) +
geom_histogram(aes(x = value)) +
facet_wrap(~ exp, scales = "free")## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
1.4 Response data: birth weight (in grams)
Y <- select(hs_data2, birth_weight) %>%
as.matrix()
head(Y)## birth_weight
## [1,] 2860
## [2,] 2755
## [3,] 3505
## [4,] 2695
## [5,] 3355
## [6,] 3810Distribution of birth weight and scaled birth weight
hist(Y, breaks = 20)
hist(scale(Y), breaks = 20)
1.5 Scatterplots of exposures and outcome (birth weight)
Both birth weight (Y) and the exposures are scaled here
NOTE: Don’t use these plots as a way to estimate how many predictors might make the cut. This should be done a priori
df <- as.data.frame(cbind(scale(Y), X.scaled))
# par(mfrow=c(5,4))
sapply(2:length(df), function(x){
lm.x <- lm(birth_weight ~ df[,x], data = df)
plot(df[,c(x, 1)],
xlab = paste0(colnames(df)[x], " beta: ",
round(summary(lm.x)$coef[2,1],4),
"; p = ",
round(summary(lm.x)$coef[2,4],4)))
abline(lm.x)
})
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## NULL2 Is gestational age a potenital mediator?
I.e., is there a relationship between our exposures and gestational age?
The DAG might look something like this:
exposures —> gestational age —> birth weight _________________________________^
2.1 Scatter plots for exposures and gestational age
Both gestational age and the exposures are scaled here. Gestational age measured in weeks from estimated date of conception to delivery
Since there were some (small) relationships between exposures and gestational age (based on simple linear regression models– namely the ozone and SES indicators), I’m going to omit this covariate for now.
df2 <- as.data.frame(cbind(W.scaled[,"gest_age_w"], X.scaled))
colnames(df2)[1] <- "gest_age_w"
# par(mfrow=c(5,4))
sapply(2:length(df2), function(x){
lm.x <- lm(gest_age_w ~ df2[,x], data = df2)
plot(df2[,c(x, 1)],
xlab = paste0(colnames(df2)[x], " beta: ",
round(summary(lm.x)$coef[2,1],4),
"; p = ",
round(summary(lm.x)$coef[2,4],4)))
abline(lm.x)
})
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## NULLDropping gest_age_w from the covariates
colnames(W.scaled)## [1] "lat" "lon" "lat_lon_int" "latina_re"
## [5] "black_re" "other_re" "ed_no_hs" "ed_hs"
## [9] "ed_aa" "ed_4yr" "low_bmi" "ovwt_bmi"
## [13] "obese_bmi" "concep_spring" "concep_summer" "concep_fall"
## [17] "concep_2010" "concep_2011" "concep_2012" "concep_2013"
## [21] "maternal_age" "any_smoker" "smokeSH" "mean_cpss"
## [25] "mean_epsd" "male" "gest_age_w"W.scaled2 <- W.scaled[,-c(ncol(W.scaled))]
colnames(W.scaled2)## [1] "lat" "lon" "lat_lon_int" "latina_re"
## [5] "black_re" "other_re" "ed_no_hs" "ed_hs"
## [9] "ed_aa" "ed_4yr" "low_bmi" "ovwt_bmi"
## [13] "obese_bmi" "concep_spring" "concep_summer" "concep_fall"
## [17] "concep_2010" "concep_2011" "concep_2012" "concep_2013"
## [21] "maternal_age" "any_smoker" "smokeSH" "mean_cpss"
## [25] "mean_epsd" "male"3 RIDGE regression
To see if there might be something going on, Lauren suggested a ridge regression with a small penalty.
set.seed(123)
library(glmnet)## Loading required package: Matrix##
## Attaching package: 'Matrix'## The following objects are masked from 'package:tidyr':
##
## expand, pack, unpack## Loaded glmnet 4.0-2lambda_seq <- 10^seq(4, -4, by = -.05)
#' Best lambda from CV
ridge_cv <- cv.glmnet(X, Y, alpha = 0, lambda = lambda_seq,
standardize = T, standardize.response = T)
plot(ridge_cv)
best_lambda <- ridge_cv$lambda.min
best_lambda## [1] 891.2509#' Fit the model using the best_lambda
bw_ridge <- glmnet(X, Y, alpha = 0, lambda = best_lambda,
standardize = T, standardize.response = T)
summary(bw_ridge)## Length Class Mode
## a0 1 -none- numeric
## beta 21 dgCMatrix S4
## df 1 -none- numeric
## dim 2 -none- numeric
## lambda 1 -none- numeric
## dev.ratio 1 -none- numeric
## nulldev 1 -none- numeric
## npasses 1 -none- numeric
## jerr 1 -none- numeric
## offset 1 -none- logical
## call 7 -none- call
## nobs 1 -none- numericRidge regression coefficients
coef(bw_ridge)## 22 x 1 sparse Matrix of class "dgCMatrix"
## s0
## (Intercept) 3756.2244127611
## mean_pm 6.5831658736
## mean_o3 -5.7909309972
## mean_temp -2.6190406717
## pct_tree_cover 0.0346391254
## pct_impervious -0.4281346032
## mean_aadt_intensity -0.0002915500
## dist_m_tri -0.0003520682
## dist_m_npl 0.0001168135
## dist_m_waste_site 0.0017447014
## dist_m_major_emit -0.0003705192
## dist_m_cafo -0.0003121004
## dist_m_mine_well -0.0022906005
## cvd_rate_adj -0.1469368176
## res_rate_adj -0.1446242346
## violent_crime_rate -0.4156388202
## property_crime_rate -0.0143345439
## pct_less_hs -0.6736508410
## pct_unemp -3.6551596165
## pct_limited_eng -0.5218862220
## pct_hh_pov -0.4758794734
## pct_poc -0.4466466437Ridge regression predictions
ridge_pred <- predict(bw_ridge, newx = X)
plot(Y, ridge_pred)
actual <- Y
preds <- ridge_pred
rsq <- 1 - (sum((preds - actual) ^ 2))/(sum((actual - mean(actual)) ^ 2))The R2 value for this model is 0.03. Based on these results, it doesn’t look like there’s much here.
4 Nonparametric Bayesian Shrinkage (NPB): Birth weight
Still, we wanted to try to fit the NPB model with these data.
4.1 Finding the NPB priors
Start with Lauren’s from the example in the vignette
In an email from April 29, Lauren provided me with some additional guidance on finding the NPB priors:
- Keep alpha.pi and beta.pi set to 1, and then let a.phi1 take values 1, 10, and 100 and see how the results change.
- Keep a.phi1 set to 1 (or 10 or 100), and mess with alpha.pi and beta.pi.
- Run the following code: alpha.pi=1 beta.pi=1 plot(density(rbeta(10000, alpha.pi, beta.pi))) and then change alpha.pi and beta.pi and see how it changes the prior distribution.
- This is the distribution of the probability of a main effect regression coefficient being 0 (aka exclusion probability). We don’t want this to be too informative (you don’t want high mass around just a few values). Also alpha.pi and beta.pi don’t have to be the same value. You might try alpha.pi = 1 and beta.pi = 2 to get a slightly lower prior probability of exclusion. Try not to change all three (alpha.pi, beta.pi, and a.phi1) at once.
- When playing with the priors, set “interact=FALSE” and just fit the modelwith the main effects. Most of the interactions were null anyway so it shouldn’t change the results too much and it will make the code run a lot faster. Then when you find a set of priors you like, you can add in “interact=TRUE” and “XWinteract=TRUE.”
Some additional feedback from Lauren during our 6/10 meeting:
- The confidence intervals were really wide and heavily skewed. I’m going to try adjusting the sig2inv.mu1 parameter after the a.phi1 parameter to see if this helps
- the rbeta distributions is interpreted as the exclusion probability, so I should try to aim to have most of the mass of that distribution in the middle, since we hypothesize that maybe 40-60% of the predictors will be important. The way to do this is to set alpha.pi and beta.pi to the same value
- I should set the burn in number to be about half the iterations
Note: I’m including far fewer iterations of the priors than in the previous version of the document.
4.1.1 Vignette Priors
set.seed(123)
priors.npb.1 <- list(alpha.pi = 1, beta.pi = 1, alpha.pi2 = 9, beta.pi2 = 1,
a.phi1 = 1)
fit.npb.1 <- npb(niter = 1000, nburn = 500, X = X.scaled, Y = Y, W = W.scaled2,
scaleY = TRUE,
priors = priors.npb.1, interact = F)
npb.sum.1 <- summary(fit.npb.1)
npb.sum.1$main.effects## Posterior Mean SD 95% CI Lower 95% CI Upper PIP
## [1,] -0.06294726 1.687109 0.0000000 0 0.030
## [2,] -0.29091146 2.551404 -2.0623012 0 0.040
## [3,] -0.39619712 4.707586 -1.5182704 0 0.032
## [4,] -0.03913962 2.358689 0.0000000 0 0.018
## [5,] -0.24478491 1.883445 0.0000000 0 0.026
## [6,] -0.02992530 1.238033 0.0000000 0 0.018
## [7,] -0.06459764 1.187282 0.0000000 0 0.022
## [8,] -0.07195478 1.626867 0.0000000 0 0.026
## [9,] 0.52187302 4.607456 0.0000000 0 0.022
## [10,] 0.15513912 2.716250 0.0000000 0 0.028
## [11,] -0.26301331 3.031174 -0.4129585 0 0.030
## [12,] -0.59623768 4.782450 -7.8170388 0 0.044
## [13,] -0.41000284 3.325195 -2.0623012 0 0.034
## [14,] -0.35348519 2.749343 -1.3278783 0 0.030
## [15,] -0.05106869 2.246354 0.0000000 0 0.030
## [16,] -0.05304155 1.567894 0.0000000 0 0.018
## [17,] -0.08577037 1.819558 0.0000000 0 0.026
## [18,] -1.15486876 6.567923 -16.6412947 0 0.054
## [19,] -0.16285021 1.546441 0.0000000 0 0.026
## [20,] -0.15357498 1.222171 0.0000000 0 0.026
## [21,] -0.27218562 2.503071 0.0000000 0 0.022plot(fit.npb.1$beta[,1], type = "l")
plot(fit.npb.1$beta[,2], type = "l")
plot(fit.npb.1$beta[,13], type = "l")
4.1.2 Adjust alpha.pi and beta.pi
For now, leave a.phi1 and sig2inv.mu1 alone for now.
alpha.pi and beta.pi are responsible for the exclusion probability distribution. If we think we want ~50% of our covariates, we need the mass of this distribution to be somewhere between 0.4 and 0.6. To do this, we set alpha.pi and beta.pi to the same value
4.1.2.1 Try making alpha.pi and beta.pi 2
plot(density(rbeta(10000, 2, 2)))
priors.npb.12 <- list(alpha.pi = 2, beta.pi = 2, alpha.pi2 = 9, beta.pi2 = 1,
a.phi1 = 1, sig2inv.mu1 = 1)
fit.npb.12 <- npb(niter = 1000, nburn = 500, X = X.scaled, Y = Y, W = W.scaled2,
scaleY = TRUE,
priors = priors.npb.12, interact = F)
npb.sum.12 <- summary(fit.npb.12)
npb.sum.12$main.effects## Posterior Mean SD 95% CI Lower 95% CI Upper PIP
## [1,] -0.05585006 2.558733 -0.9107843 1.2488176 0.064
## [2,] -1.18895021 6.461003 -19.2446984 0.0000000 0.078
## [3,] -0.96419729 5.568817 -16.7861820 0.0000000 0.082
## [4,] -0.17391929 3.339516 -3.8588587 0.0000000 0.056
## [5,] -0.37209500 3.188349 -4.1881190 0.0000000 0.052
## [6,] 0.01243140 2.401382 -1.1337072 0.0000000 0.052
## [7,] -0.05330369 2.623531 -0.8095384 0.0000000 0.050
## [8,] 0.02179721 1.330539 -0.3965023 0.0000000 0.050
## [9,] 1.04072127 7.198161 0.0000000 10.5356040 0.066
## [10,] 0.03250576 1.233531 0.0000000 0.0000000 0.046
## [11,] -0.49881936 4.284310 -6.5704159 0.0000000 0.070
## [12,] -1.13807809 6.103752 -19.1306487 0.0000000 0.094
## [13,] -0.48738699 3.979972 -5.6423561 0.0000000 0.064
## [14,] -0.52923656 4.432090 -7.3351997 0.0000000 0.068
## [15,] -0.20711733 2.605385 -2.0372706 0.0000000 0.048
## [16,] -0.23005353 2.320961 -2.0372706 0.0000000 0.056
## [17,] -0.17426309 2.017873 -4.4027432 0.0000000 0.056
## [18,] -2.81786531 10.058263 -42.6622076 0.0000000 0.122
## [19,] -0.21014274 2.756962 -1.8169934 0.0000000 0.050
## [20,] -0.22612120 1.957105 -2.0821434 0.0000000 0.050
## [21,] -0.19384788 2.641713 -4.0618985 0.1994985 0.064plot(fit.npb.12$beta[,1], type = "l")
plot(fit.npb.12$beta[,2], type = "l")
plot(fit.npb.12$beta[,13], type = "l")
4.1.2.2 Try making alpha.pi and beta.pi 5
plot(density(rbeta(10000, 5, 5)))
priors.npb.13 <- list(alpha.pi = 5, beta.pi = 5, alpha.pi2 = 9, beta.pi2 = 1,
a.phi1 = 1, sig2inv.mu1 = 1)
fit.npb.13 <- npb(niter = 1000, nburn = 500, X = X.scaled, Y = Y, W = W.scaled2,
scaleY = TRUE,
priors = priors.npb.13, interact = F)
npb.sum.13 <- summary(fit.npb.13)
npb.sum.13$main.effects## Posterior Mean SD 95% CI Lower 95% CI Upper PIP
## [1,] -0.1739327 4.490772 -10.213958 9.9368147 0.188
## [2,] -1.4247428 8.176458 -16.181675 8.1882486 0.222
## [3,] -1.4403640 6.221568 -20.696307 4.3895425 0.216
## [4,] -0.3358477 4.528988 -9.591430 7.7615128 0.216
## [5,] -0.9969214 5.066390 -14.631366 3.8872951 0.202
## [6,] -0.1445406 3.433180 -8.468007 6.7668174 0.196
## [7,] -0.3991079 4.911675 -12.022636 10.2419437 0.216
## [8,] 0.1189375 5.215748 -8.108638 11.3293838 0.184
## [9,] 1.6358856 7.205395 -6.027428 25.5745080 0.232
## [10,] 0.3000110 3.435584 -5.658070 11.4664392 0.192
## [11,] -1.3901896 8.247625 -20.467505 6.5096500 0.214
## [12,] -1.4442944 6.338596 -20.938242 6.3300568 0.240
## [13,] -1.3257189 6.613639 -19.727254 4.3277879 0.224
## [14,] -1.3544745 5.246391 -16.688737 1.9619716 0.218
## [15,] 0.0139276 3.685508 -7.697730 5.4654433 0.172
## [16,] -1.0157786 4.059599 -13.367519 1.8186189 0.182
## [17,] -0.7172938 6.373838 -12.879427 4.3895425 0.202
## [18,] -3.4726949 9.571950 -34.045190 2.1210054 0.294
## [19,] -0.8775056 4.320639 -12.681860 3.3689995 0.196
## [20,] -0.7384011 3.524475 -11.224363 0.7593049 0.164
## [21,] -0.3347857 2.815050 -8.065163 3.0029989 0.166plot(fit.npb.13$beta[,1], type = "l")
plot(fit.npb.13$beta[,2], type = "l")
plot(fit.npb.13$beta[,13], type = "l")
4.1.2.3 Try making alpha.pi and beta.pi 8
plot(density(rbeta(10000, 8, 8)))
priors.npb.14 <- list(alpha.pi = 8, beta.pi = 8, alpha.pi2 = 9, beta.pi2 = 1,
a.phi1 = 1, sig2inv.mu1 = 1)
fit.npb.14 <- npb(niter = 1000, nburn = 500, X = X.scaled, Y = Y, W = W.scaled2,
scaleY = TRUE,
priors = priors.npb.14, interact = F)
npb.sum.14 <- summary(fit.npb.14)
npb.sum.14$main.effects## Posterior Mean SD 95% CI Lower 95% CI Upper PIP
## [1,] -0.7542073 4.727682 -13.375772 9.369699 0.304
## [2,] -3.0212801 9.232142 -30.064091 5.032394 0.362
## [3,] -1.2184191 6.055311 -16.912434 8.907677 0.300
## [4,] -0.8547605 5.402424 -14.998936 8.390509 0.288
## [5,] -1.3986793 5.953325 -17.081301 4.853341 0.276
## [6,] -0.5251034 4.559356 -12.719423 9.369699 0.262
## [7,] -0.7089094 5.409248 -13.043111 9.241721 0.294
## [8,] 0.1735833 6.132190 -9.558869 14.202827 0.290
## [9,] 1.4331513 8.023282 -8.366645 23.124217 0.280
## [10,] -0.2391486 4.648372 -11.790578 9.571535 0.278
## [11,] -1.8979572 7.780447 -22.351703 8.666068 0.336
## [12,] -2.1739360 7.330178 -25.275595 8.758575 0.388
## [13,] -1.7110317 6.148423 -17.052794 4.839192 0.294
## [14,] -1.8875976 5.800864 -15.372856 3.905622 0.304
## [15,] -0.4933873 3.705164 -10.128855 5.771647 0.224
## [16,] -1.4644885 5.293402 -16.840640 4.853341 0.290
## [17,] -1.5884687 4.980539 -16.912434 4.806950 0.314
## [18,] -5.3458715 12.474886 -47.674022 3.972676 0.418
## [19,] -1.0264207 5.150193 -15.429091 7.863305 0.296
## [20,] -0.9030834 4.267366 -12.228600 6.677137 0.272
## [21,] -0.8473787 4.576029 -12.281218 6.497990 0.274plot(fit.npb.14$beta[,1], type = "l")
plot(fit.npb.14$beta[,2], type = "l")
plot(fit.npb.14$beta[,13], type = "l")
4.1.3 Set alpha.pi and beta.pi to 5, readjust a.phi1 and sig2inv.mu1
Set alpha.pi and beta.pi to 5, rather than 8, and try adjusting a.phi1 and sig2inv.mu1
4.1.3.1 Try making a.phi1 = 10 and sig2inv.mu1 = 1
priors.npb.23 <- list(alpha.pi = 5, beta.pi = 5, alpha.pi2 = 9, beta.pi2 = 1,
a.phi1 = 10, sig2inv.mu1 = 1)
fit.npb.23 <- npb(niter = 1000, nburn = 500, X = X.scaled, Y = Y, W = W.scaled2,
scaleY = TRUE,
priors = priors.npb.23, interact = F)
npb.sum.23 <- summary(fit.npb.23)
npb.sum.23$main.effects## Posterior Mean SD 95% CI Lower 95% CI Upper PIP
## [1,] -0.5873083 4.918398 -12.342901 8.711006 0.246
## [2,] -3.8048904 13.456931 -39.722335 5.668791 0.332
## [3,] -1.6873544 7.578959 -16.168928 5.668321 0.300
## [4,] -0.3056229 4.523096 -10.595951 7.953071 0.244
## [5,] -1.2289691 5.306702 -14.074921 5.736699 0.280
## [6,] -0.1743268 4.616332 -10.091337 9.432144 0.252
## [7,] -0.3454703 5.704442 -11.607307 16.708223 0.260
## [8,] -0.1315553 5.063896 -9.860011 10.799674 0.232
## [9,] 2.4614174 9.930215 -7.405537 37.951814 0.308
## [10,] 0.2377121 4.839663 -9.722982 11.712248 0.230
## [11,] -4.1208739 21.528436 -52.278068 11.932845 0.352
## [12,] -2.3069329 8.236088 -24.465618 6.055165 0.326
## [13,] -1.3318387 5.953807 -16.819478 7.907002 0.278
## [14,] -1.7582919 6.385090 -18.183169 5.668791 0.284
## [15,] -0.5116488 4.584157 -9.937609 5.839274 0.240
## [16,] -1.4645731 5.161296 -15.815723 5.525176 0.294
## [17,] -1.2366149 6.005428 -18.133263 5.870796 0.260
## [18,] -5.2824150 13.446943 -49.920837 3.103663 0.366
## [19,] -0.6781444 4.791220 -12.897476 7.609749 0.258
## [20,] -0.6484217 5.260639 -13.456143 8.180968 0.248
## [21,] -0.6545086 4.834557 -11.437506 6.286956 0.222plot(fit.npb.23$beta[,1], type = "l")
plot(fit.npb.23$beta[,2], type = "l")
plot(fit.npb.23$beta[,13], type = "l")
4.1.3.2 Try making a.phi1 = 10 and sig2inv.mu1 = 10
priors.npb.24 <- list(alpha.pi = 5, beta.pi = 5, alpha.pi2 = 9, beta.pi2 = 1,
a.phi1 = 10, sig2inv.mu1 = 10)
fit.npb.24 <- npb(niter = 1000, nburn = 500, X = X.scaled, Y = Y, W = W.scaled2,
scaleY = TRUE,
priors = priors.npb.24, interact = F)
npb.sum.24 <- summary(fit.npb.24)
npb.sum.24$main.effects## Posterior Mean SD 95% CI Lower 95% CI Upper PIP
## [1,] -0.2602480 6.321456 -13.744945 13.838969 0.260
## [2,] -2.9383247 10.328329 -36.545051 7.628224 0.316
## [3,] -1.3957413 7.009138 -20.979797 9.520137 0.290
## [4,] -0.2305071 5.067001 -12.707187 10.119051 0.250
## [5,] -1.2506499 6.225976 -18.573920 6.773117 0.250
## [6,] -0.1414881 4.242075 -9.397693 8.396127 0.226
## [7,] -0.4909395 5.925732 -12.959531 10.107668 0.244
## [8,] 0.2986060 5.456119 -10.368056 13.646438 0.262
## [9,] 3.7845724 12.155981 -5.949447 51.084993 0.312
## [10,] 0.7249301 6.134249 -8.188400 16.691562 0.258
## [11,] -1.0511460 15.923305 -24.977724 23.721207 0.344
## [12,] -1.8498651 7.316253 -24.546506 7.505480 0.272
## [13,] -0.9879859 5.686595 -15.871228 5.777184 0.254
## [14,] -2.1277142 7.975941 -23.293444 5.168810 0.274
## [15,] -0.4265771 4.214481 -10.174425 7.653653 0.218
## [16,] -1.1747947 5.568738 -18.464146 9.101806 0.286
## [17,] -1.4413812 5.728937 -18.138404 4.856576 0.276
## [18,] -6.2212032 14.097082 -53.785694 2.011623 0.364
## [19,] -0.5736030 4.600584 -12.862286 8.285742 0.242
## [20,] -0.7877488 5.438677 -14.547267 9.016658 0.230
## [21,] -0.2710370 5.503657 -12.348355 9.848989 0.238plot(fit.npb.24$beta[,1], type = "l")
plot(fit.npb.24$beta[,2], type = "l")
plot(fit.npb.24$beta[,13], type = "l")
4.2 Fit the NPB model without temperature
Below I’ve used the set of priors labeled “24” and set scaleY = T
The priors are as follows: r priors.npb.24
Note that this version of the model does not include gest_age_w. It does include an indicator variable for season of conception (ref = winter) and the lon/lat as covariates and the percentage of the census tract population that is not NHW as an exposure.
priors.npb <- priors.npb.24
#' Exposures (minus temperature)
colnames(X.scaled)## [1] "mean_pm" "mean_o3" "mean_temp"
## [4] "pct_tree_cover" "pct_impervious" "mean_aadt_intensity"
## [7] "dist_m_tri" "dist_m_npl" "dist_m_waste_site"
## [10] "dist_m_major_emit" "dist_m_cafo" "dist_m_mine_well"
## [13] "cvd_rate_adj" "res_rate_adj" "violent_crime_rate"
## [16] "property_crime_rate" "pct_less_hs" "pct_unemp"
## [19] "pct_limited_eng" "pct_hh_pov" "pct_poc"#' Covariates
colnames(W.scaled2)## [1] "lat" "lon" "lat_lon_int" "latina_re"
## [5] "black_re" "other_re" "ed_no_hs" "ed_hs"
## [9] "ed_aa" "ed_4yr" "low_bmi" "ovwt_bmi"
## [13] "obese_bmi" "concep_spring" "concep_summer" "concep_fall"
## [17] "concep_2010" "concep_2011" "concep_2012" "concep_2013"
## [21] "maternal_age" "any_smoker" "smokeSH" "mean_cpss"
## [25] "mean_epsd" "male"# fit.npb <- npb(niter = 5000, nburn = 2500, X = X.scaled[,-c(3)], Y = Y, W = W.scaled2,
# scaleY = TRUE,
# priors = priors.npb, interact = TRUE, XWinteract = TRUE)
# save(fit.npb, file = here::here("Results", "NPB_Birth_Weight_v4.1.rdata"))
load(here::here("Results", "NPB_Birth_Weight_v4.1.rdata"))
npb.sum <- summary(fit.npb)4.2.1 First, main effect regression coefficients with PIPs
rownames(npb.sum$main.effects) <- colnames(X.scaled[,-c(3)])
npb.sum$main.effects## Posterior Mean SD 95% CI Lower 95% CI Upper PIP
## mean_pm -0.39311629 5.948287 -13.793001 10.7646248 0.1812
## mean_o3 -133.45924031 95.282493 -280.870320 1.4166975 0.8032
## pct_tree_cover 0.12721285 5.311107 -10.223723 12.6643926 0.1780
## pct_impervious -0.70088765 5.123154 -14.188222 6.4138402 0.1800
## mean_aadt_intensity 0.35475982 5.230087 -8.714796 13.2645464 0.1668
## dist_m_tri -0.18341960 5.428993 -12.867837 11.6968190 0.1776
## dist_m_npl 0.55391982 5.969792 -8.463951 16.7125172 0.1728
## dist_m_waste_site 3.43354109 11.364150 -4.896414 42.6424558 0.2272
## dist_m_major_emit 0.67721995 5.837771 -8.351270 16.6815966 0.1696
## dist_m_cafo -1.63593647 18.422799 -40.210811 22.7887508 0.2388
## dist_m_mine_well -1.71586374 7.465745 -24.795214 7.3103901 0.2196
## cvd_rate_adj -0.95469604 6.845516 -18.333719 6.3757417 0.1948
## res_rate_adj -2.00711286 8.311984 -25.072347 3.7978670 0.2128
## violent_crime_rate -0.01728102 4.902578 -10.898684 12.6340426 0.1644
## property_crime_rate -1.07099605 5.323785 -16.716705 4.8809724 0.1820
## pct_less_hs -0.69940998 6.130446 -16.760072 9.3378765 0.2052
## pct_unemp -7.40692974 16.622892 -58.385635 0.7882151 0.3300
## pct_limited_eng -0.52770287 5.713158 -13.794315 8.9179180 0.1820
## pct_hh_pov -0.59773462 6.363955 -16.122840 8.7457755 0.1772
## pct_poc 0.30759474 6.638556 -10.919232 15.5608535 0.17724.2.2 Next, posterior means and CIs for covariates
rownames(npb.sum$covariates)[2:nrow(npb.sum$covariates)] <- colnames(W.scaled2)
npb.sum$covariates## Posterior Mean SD 95% CI Lower 95% CI Upper
## <NA> 3188.497757 222.23968 2745.249590 3606.114527
## lat 3.087748 326.74078 -650.881049 649.864018
## lon 13.535619 155.17252 -293.948785 316.709585
## lat_lon_int 13.476969 394.38967 -775.570358 792.296411
## latina_re -104.065035 49.39609 -199.176137 -3.928516
## black_re -286.353899 52.65678 -387.893361 -179.885528
## other_re -94.757408 69.28834 -229.408383 46.382939
## ed_no_hs 167.996529 78.22937 12.811265 326.074135
## ed_hs 133.910182 68.53541 -1.411717 266.147028
## ed_aa 75.765854 60.83075 -42.644626 194.743071
## ed_4yr 78.732650 50.57320 -18.453706 174.391137
## low_bmi -70.272816 91.20097 -248.873010 108.716295
## ovwt_bmi 43.853229 40.67039 -33.169202 123.784296
## obese_bmi 116.361817 46.89326 26.091002 212.596238
## concep_spring -102.784891 95.46952 -247.156596 116.067130
## concep_summer -92.677221 133.71853 -359.007086 119.923017
## concep_fall -27.171801 89.25950 -202.963118 129.727359
## concep_2010 48.076553 218.31333 -387.714076 478.048424
## concep_2011 42.028775 217.92803 -396.343367 475.711417
## concep_2012 40.952192 219.48805 -389.942122 474.851589
## concep_2013 117.428601 217.86526 -315.892264 550.794508
## maternal_age 62.600170 22.37894 18.284726 105.908163
## any_smoker -126.840859 64.89488 -254.440824 0.403685
## smokeSH -106.466403 44.89779 -192.668553 -17.789113
## mean_cpss 8.973756 19.93426 -31.452112 47.007042
## mean_epsd -51.348427 20.14631 -89.804097 -11.042824
## male 170.342338 32.99507 103.917658 236.0614114.2.3 Interactions
Next, all of the interactions between exposures or between exposures and covariates
npb.sum$interactions## Posterior Mean SD 95% CI Lower 95% CI Upper PIP
## [1,] 0.077512245499 1.89496902 0.0000 0.0000 0.0036
## [2,] -0.005298254770 0.16183541 0.0000 0.0000 0.0016
## [3,] -0.001160855197 0.10434367 0.0000 0.0000 0.0016
## [4,] 0.018777573001 0.80899803 0.0000 0.0000 0.0020
## [5,] -0.008397274677 0.22122332 0.0000 0.0000 0.0028
## [6,] -0.009954516915 0.33661058 0.0000 0.0000 0.0028
## [7,] -0.017486523183 0.48198359 0.0000 0.0000 0.0024
## [8,] -0.022295212401 0.62083315 0.0000 0.0000 0.0040
## [9,] -0.038337018229 0.87255923 0.0000 0.0000 0.0064
## [10,] -0.022562657529 0.56250101 0.0000 0.0000 0.0060
## [11,] -0.006885025261 0.19264045 0.0000 0.0000 0.0016
## [12,] -0.017422756289 0.57495746 0.0000 0.0000 0.0024
## [13,] -0.008001421013 0.27600655 0.0000 0.0000 0.0032
## [14,] -0.021756743249 0.41111900 0.0000 0.0000 0.0060
## [15,] -0.015524688102 0.53380824 0.0000 0.0000 0.0012
## [16,] -0.018793646043 0.49327965 0.0000 0.0000 0.0036
## [17,] -0.018369868490 0.40306195 0.0000 0.0000 0.0032
## [18,] -0.006740261188 0.23711426 0.0000 0.0000 0.0020
## [19,] -0.019959681945 0.56628631 0.0000 0.0000 0.0028
## [20,] -0.043354340685 1.03737057 0.0000 0.0000 0.0052
## [21,] -0.015333683037 0.39445346 0.0000 0.0000 0.0040
## [22,] -0.019971193952 0.54992357 0.0000 0.0000 0.0028
## [23,] -0.095180540938 1.97478195 0.0000 0.0000 0.0056
## [24,] -0.036270396704 0.85726619 0.0000 0.0000 0.0048
## [25,] -0.038615863869 0.91345921 0.0000 0.0000 0.0064
## [26,] -0.006761029442 0.55120606 0.0000 0.0000 0.0032
## [27,] -0.036809623474 0.84759368 0.0000 0.0000 0.0052
## [28,] -0.025083023398 0.80142309 0.0000 0.0000 0.0040
## [29,] 0.007553754461 0.22185302 0.0000 0.0000 0.0028
## [30,] -0.001200522442 0.06643487 0.0000 0.0000 0.0012
## [31,] 0.000176397720 0.51778312 0.0000 0.0000 0.0020
## [32,] -0.008181183832 0.31138968 0.0000 0.0000 0.0040
## [33,] 0.010033332885 0.65362821 0.0000 0.0000 0.0028
## [34,] -0.009695057530 0.21646088 0.0000 0.0000 0.0036
## [35,] 0.005076217196 0.48059341 0.0000 0.0000 0.0016
## [36,] 0.059769235885 1.41738566 0.0000 0.0000 0.0044
## [37,] 0.017421036520 0.81440692 0.0000 0.0000 0.0020
## [38,] -0.008407800031 0.22382709 0.0000 0.0000 0.0020
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## [231,] 125.316644805642 165.76860874 0.0000 421.2932 0.3788
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## [300,] 0.018079525846 1.23574077 0.0000 0.0000 0.0036
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## [305,] 0.009655037266 0.50448854 0.0000 0.0000 0.0036
## [306,] -0.051756361217 1.20456760 0.0000 0.0000 0.0032
## [307,] 0.023146107980 1.97622196 0.0000 0.0000 0.0036
## [308,] -0.020261138479 0.48772513 0.0000 0.0000 0.0044
## [309,] -0.006048449287 0.36604985 0.0000 0.0000 0.0028
## [310,] -0.003036588924 0.51232017 0.0000 0.0000 0.0032
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## [314,] 0.019242669204 1.22957977 0.0000 0.0000 0.0032
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## [584,] 0.008152163610 0.55528023 0.0000 0.0000 0.0032
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## [591,] -0.004649083400 0.25496328 0.0000 0.0000 0.0040
## [592,] 0.045989309754 1.54812278 0.0000 0.0000 0.0028
## [593,] -0.024345876969 0.62356136 0.0000 0.0000 0.0032
## [594,] -0.032672501055 0.82374121 0.0000 0.0000 0.0032
## [595,] -0.020045275100 0.45435262 0.0000 0.0000 0.0036
## [596,] -0.017751756048 0.42098731 0.0000 0.0000 0.0028
## [597,] -0.004200200904 0.12712235 0.0000 0.0000 0.0028
## [598,] -0.032053802515 0.79772780 0.0000 0.0000 0.0036
## [599,] 0.016842502887 1.15927199 0.0000 0.0000 0.0036
## [600,] -0.070318349761 2.34183355 0.0000 0.0000 0.0036
## [601,] -0.009934425937 0.22625343 0.0000 0.0000 0.0028
## [602,] -0.003822300287 0.25921719 0.0000 0.0000 0.0032
## [603,] 0.078653606168 3.22467748 0.0000 0.0000 0.0052
## [604,] -0.008605321340 0.20144946 0.0000 0.0000 0.0028
## [605,] -0.004510164259 0.14325420 0.0000 0.0000 0.0016
## [606,] -0.034148517363 1.38981093 0.0000 0.0000 0.0032
## [607,] -0.004578201489 0.15501365 0.0000 0.0000 0.0012
## [608,] -0.046768490188 1.05353002 0.0000 0.0000 0.0048
## [609,] -0.009612838960 0.25317189 0.0000 0.0000 0.0020
## [610,] -0.009443713908 0.30636062 0.0000 0.0000 0.0040
## [611,] -0.031408458855 0.75666644 0.0000 0.0000 0.0036
## [612,] 0.012237555232 0.70421566 0.0000 0.0000 0.0016
## [613,] -0.041370550266 1.41840911 0.0000 0.0000 0.0040
## [614,] 0.016212102270 1.44872369 0.0000 0.0000 0.0048
## [615,] -0.013145600858 0.29685104 0.0000 0.0000 0.0036
## [616,] -0.169625771841 3.55407620 0.0000 0.0000 0.0048
## [617,] -0.039240453614 1.88188869 0.0000 0.0000 0.0012
## [618,] -0.005269214571 0.13439005 0.0000 0.0000 0.0020
## [619,] -0.003076526626 0.11242850 0.0000 0.0000 0.0008
## [620,] -0.057347446895 1.72495953 0.0000 0.0000 0.0040
## [621,] -0.011371596143 0.98735479 0.0000 0.0000 0.0048
## [622,] -0.250565496010 5.10554648 0.0000 0.0000 0.0048
## [623,] -0.009690965036 0.27072685 0.0000 0.0000 0.0024
## [624,] -0.057029533979 1.43915305 0.0000 0.0000 0.0056
## [625,] -0.007817776412 0.28733881 0.0000 0.0000 0.0048
## [626,] -0.007797170403 0.31795585 0.0000 0.0000 0.0024
## [627,] -0.006623926491 0.15153783 0.0000 0.0000 0.0032
## [628,] -0.100584447923 3.30292160 0.0000 0.0000 0.0032
## [629,] -0.000750548337 1.86389532 0.0000 0.0000 0.0024
## [630,] -0.009994159569 0.28833917 0.0000 0.0000 0.0024
## [631,] -0.008820477452 0.29645074 0.0000 0.0000 0.0028
## [632,] -0.135969615972 2.92828590 0.0000 0.0000 0.0052
## [633,] -0.046100760987 1.31614838 0.0000 0.0000 0.0040
## [634,] -0.030565850949 0.86583021 0.0000 0.0000 0.0036
## [635,] -0.004687051834 0.16612548 0.0000 0.0000 0.0012
## [636,] -0.014218244861 0.29578696 0.0000 0.0000 0.0044
## [637,] -0.024397549719 0.69739803 0.0000 0.0000 0.0028
## [638,] -0.009109701633 0.30240794 0.0000 0.0000 0.0032
## [639,] -0.015944040292 0.45663594 0.0000 0.0000 0.0040
## [640,] 0.005106850522 0.44492338 0.0000 0.0000 0.0032
## [641,] -0.034725268937 1.05783585 0.0000 0.0000 0.0036
## [642,] -0.002950209840 0.09647124 0.0000 0.0000 0.0016
## [643,] -0.006754035141 0.23679572 0.0000 0.0000 0.0032
## [644,] -0.005597849972 0.45902215 0.0000 0.0000 0.0028
## [645,] -0.008401471546 0.21035583 0.0000 0.0000 0.0024
## [646,] -0.074121482245 2.40581668 0.0000 0.0000 0.0048
## [647,] -0.000425346588 0.02126733 0.0000 0.0000 0.0004
## [648,] 0.000790630084 1.23113757 0.0000 0.0000 0.0052
## [649,] 0.000432618888 0.45784420 0.0000 0.0000 0.0028
## [650,] -0.145741880389 3.06906657 0.0000 0.0000 0.0060
## [651,] -0.003172104505 0.15537365 0.0000 0.0000 0.0024
## [652,] -0.046685507757 2.12214954 0.0000 0.0000 0.0020
## [653,] -0.006322497032 0.44991788 0.0000 0.0000 0.0028
## [654,] -0.009285743890 0.37759836 0.0000 0.0000 0.0016
## [655,] -0.019928334809 0.45214208 0.0000 0.0000 0.0052
## [656,] -0.008927225596 0.30104603 0.0000 0.0000 0.0028
## [657,] -0.007741397982 0.39154993 0.0000 0.0000 0.0028
## [658,] 0.001901749969 0.49295936 0.0000 0.0000 0.0032
## [659,] -0.000902512254 0.46114259 0.0000 0.0000 0.0024
## [660,] -0.023507615978 0.78984557 0.0000 0.0000 0.0020
## [661,] -0.013813288202 0.28322338 0.0000 0.0000 0.0040
## [662,] -0.013262506029 0.89450226 0.0000 0.0000 0.0028
## [663,] -0.007781624225 0.34611303 0.0000 0.0000 0.0028
## [664,] -0.010712713851 0.30412599 0.0000 0.0000 0.0028
## [665,] -0.020013209795 0.48264855 0.0000 0.0000 0.0044
## [666,] -0.020541068779 0.67968047 0.0000 0.0000 0.0028
## [667,] -0.002081986442 0.66398277 0.0000 0.0000 0.0032
## [668,] -0.001262570350 0.19777942 0.0000 0.0000 0.0036
## [669,] -0.125840149299 4.35283419 0.0000 0.0000 0.0036
## [670,] -0.031285405701 0.80892019 0.0000 0.0000 0.0040
## [671,] -0.007278798419 0.16380178 0.0000 0.0000 0.0028
## [672,] -0.010209893880 0.23977147 0.0000 0.0000 0.0040
## [673,] 0.009811294667 1.27920515 0.0000 0.0000 0.0040
## [674,] -0.007947498264 0.34641686 0.0000 0.0000 0.0028
## [675,] -0.005791236191 0.29189248 0.0000 0.0000 0.0020
## [676,] -0.053490016820 1.63004683 0.0000 0.0000 0.0040
## [677,] 0.194583478820 4.10970132 0.0000 0.0000 0.0056
## [678,] -0.043785140039 1.74606556 0.0000 0.0000 0.0028
## [679,] -0.003447889209 0.14727196 0.0000 0.0000 0.0032
## [680,] -0.008915141107 0.22148593 0.0000 0.0000 0.0020
## [681,] 0.017033912052 0.90012528 0.0000 0.0000 0.0044
## [682,] -0.017604969427 0.78929270 0.0000 0.0000 0.0040
## [683,] -0.027235175958 0.66938179 0.0000 0.0000 0.0044
## [684,] -0.032355980424 1.12553618 0.0000 0.0000 0.0028
## [685,] -0.017507957697 0.37029523 0.0000 0.0000 0.0032
## [686,] -0.048300964822 0.89400333 0.0000 0.0000 0.0052
## [687,] -0.011742198467 0.31410257 0.0000 0.0000 0.0032
## [688,] -0.015020094874 0.52608758 0.0000 0.0000 0.0032
## [689,] -0.018215787255 0.73945197 0.0000 0.0000 0.0016
## [690,] -0.009254200946 0.26726327 0.0000 0.0000 0.0020
## [691,] 0.005392508159 0.62818751 0.0000 0.0000 0.0040
## [692,] 0.038890417125 1.94198815 0.0000 0.0000 0.0028
## [693,] -0.008626612042 0.30274520 0.0000 0.0000 0.0032
## [694,] -0.015015194116 0.36140886 0.0000 0.0000 0.0056
## [695,] 0.000175715370 0.67762016 0.0000 0.0000 0.0024
## [696,] 0.030391267528 1.92721371 0.0000 0.0000 0.0032
## [697,] -0.007146066126 0.28393743 0.0000 0.0000 0.0036
## [698,] -0.018913558711 0.47086016 0.0000 0.0000 0.0028
## [699,] -0.009935667563 0.49938961 0.0000 0.0000 0.0036
## [700,] -0.009733700596 0.38928790 0.0000 0.0000 0.0044
## [701,] -0.021805086197 0.67868523 0.0000 0.0000 0.0036
## [702,] -0.377516491970 6.38360871 0.0000 0.0000 0.0068
## [703,] 0.609401326224 8.00923605 0.0000 0.0000 0.0088
## [704,] -0.030746065683 0.66310359 0.0000 0.0000 0.0032
## [705,] -0.013508532989 0.29500978 0.0000 0.0000 0.0028
## [706,] -0.002214658920 0.55678281 0.0000 0.0000 0.0048
## [707,] -0.003227728786 0.14044609 0.0000 0.0000 0.0012
## [708,] -0.025124426510 0.56978955 0.0000 0.0000 0.0044
## [709,] -0.011770054975 0.33177240 0.0000 0.0000 0.0032
## [710,] -0.008673496365 0.24258536 0.0000 0.0000 0.00564.2.4 Predict fitted values for each individual
pred.npb <- predict(fit.npb)
fittedvals <- pred.npb$fitted.vals4.2.5 Plot predicted outcomes against “measured” outcomes
plot(fittedvals, Y)
abline(a = 0, b = 1, col = "red")
4.3 Run the NPB model with temperaure and ozone
Below I’ve used the set of priors labeled “24” and set scaleY = T
The priors are as follows: r priors.npb.24
Note that this version of the model does not include gest_age_w. It does include an indicator variable for season of conception (ref = winter) and the lon/lat as covariates and the percentage of the census tract population that is not NHW as an exposure.
priors.npb <- priors.npb.24
#' Exposures (minus temperature)
colnames(X.scaled)## [1] "mean_pm" "mean_o3" "mean_temp"
## [4] "pct_tree_cover" "pct_impervious" "mean_aadt_intensity"
## [7] "dist_m_tri" "dist_m_npl" "dist_m_waste_site"
## [10] "dist_m_major_emit" "dist_m_cafo" "dist_m_mine_well"
## [13] "cvd_rate_adj" "res_rate_adj" "violent_crime_rate"
## [16] "property_crime_rate" "pct_less_hs" "pct_unemp"
## [19] "pct_limited_eng" "pct_hh_pov" "pct_poc"#' Covariates
colnames(W.scaled2)## [1] "lat" "lon" "lat_lon_int" "latina_re"
## [5] "black_re" "other_re" "ed_no_hs" "ed_hs"
## [9] "ed_aa" "ed_4yr" "low_bmi" "ovwt_bmi"
## [13] "obese_bmi" "concep_spring" "concep_summer" "concep_fall"
## [17] "concep_2010" "concep_2011" "concep_2012" "concep_2013"
## [21] "maternal_age" "any_smoker" "smokeSH" "mean_cpss"
## [25] "mean_epsd" "male"# fit.npb2 <- npb(niter = 5000, nburn = 2500, X = X.scaled, Y = Y, W = W.scaled2,
# scaleY = TRUE,
# priors = priors.npb, interact = TRUE, XWinteract = TRUE)
# save(fit.npb2, file = here::here("Results", "NPB_Birth_Weight_v4.2.rdata"))
load(here::here("Results", "NPB_Birth_Weight_v4.2.rdata"))
npb.sum2 <- summary(fit.npb2)4.3.1 First, main effect regression coefficients with PIPs
rownames(npb.sum2$main.effects) <- colnames(X.scaled)
npb.sum2$main.effects## Posterior Mean SD 95% CI Lower 95% CI Upper PIP
## mean_pm -2.39072192 9.792126 -29.271869 8.534157 0.3064
## mean_o3 -6.38650708 23.092058 -65.112302 6.938996 0.3712
## mean_temp 13.08988731 48.534890 -18.587026 189.293128 0.3804
## pct_tree_cover -0.35132165 5.328952 -12.137421 11.560674 0.2528
## pct_impervious -0.71579581 5.075087 -14.363937 7.427655 0.2476
## mean_aadt_intensity 0.70135685 5.889176 -8.973130 18.216043 0.2392
## dist_m_tri -1.09951786 6.231821 -18.891336 8.900200 0.2728
## dist_m_npl -0.01654537 6.339152 -11.705638 14.574608 0.2604
## dist_m_waste_site 3.02530578 10.570529 -7.380639 39.172809 0.3056
## dist_m_major_emit 0.04946465 5.249829 -10.655397 13.058661 0.2368
## dist_m_cafo -2.08149176 15.148641 -31.012868 14.249976 0.3364
## dist_m_mine_well -1.72250145 7.385683 -22.594290 8.900200 0.3096
## cvd_rate_adj -1.39496856 6.112685 -18.356038 5.931195 0.2764
## res_rate_adj -2.46954801 7.830513 -26.805916 4.985631 0.3028
## violent_crime_rate -0.28237724 5.442212 -12.212582 9.176109 0.2544
## property_crime_rate -1.45733604 5.778188 -18.269563 5.210600 0.2768
## pct_less_hs -1.11592115 7.050666 -17.899684 10.643142 0.2916
## pct_unemp -6.62599040 14.516231 -51.310175 2.495315 0.3968
## pct_limited_eng -1.01024567 5.640255 -16.184771 6.906877 0.2500
## pct_hh_pov -1.06713407 5.614263 -14.965020 6.580130 0.2624
## pct_poc -0.54972375 5.929487 -13.117756 12.632636 0.25964.3.2 Next, posterior means and CIs for covariates
rownames(npb.sum2$covariates)[2:nrow(npb.sum2$covariates)] <- colnames(W.scaled2)
npb.sum2$covariates## Posterior Mean SD 95% CI Lower 95% CI Upper
## <NA> 3193.7618426 214.08586 2761.1813548 3599.488950
## lat 15.1149441 316.40057 -593.6507767 625.429608
## lon -2.6771413 149.70144 -298.6180694 290.371488
## lat_lon_int 21.8464904 381.34096 -705.2173484 763.438323
## latina_re -95.1972537 45.84762 -187.5951354 -8.004110
## black_re -280.9812933 49.23894 -380.1127023 -185.707098
## other_re -88.5646343 66.14664 -216.8151409 38.196716
## ed_no_hs 150.7201661 73.98753 3.0301253 293.719625
## ed_hs 131.0362955 67.05633 0.7066977 261.478676
## ed_aa 72.2292745 58.48073 -47.5030638 186.192993
## ed_4yr 84.5971774 50.85281 -15.0838808 177.138394
## low_bmi -70.9504190 89.15951 -242.1530260 100.826584
## ovwt_bmi 46.3377733 39.57380 -30.5937875 126.178045
## obese_bmi 124.6250030 43.84296 38.4141328 212.773111
## concep_spring -90.0244243 50.05849 -186.6334720 8.125969
## concep_summer -37.5154629 72.86750 -192.3563552 88.147847
## concep_fall 52.3501831 66.40871 -62.3703284 212.500822
## concep_2010 22.7204744 214.41234 -386.5064186 449.858775
## concep_2011 20.3041809 212.80901 -393.8430236 439.537648
## concep_2012 61.1951191 214.34672 -339.7237028 488.864472
## concep_2013 124.0019262 214.14791 -281.5454686 550.717702
## maternal_age 54.8350012 21.66444 10.9579504 96.992770
## any_smoker -147.7909204 62.18029 -268.6453560 -28.000693
## smokeSH -75.9751280 43.33558 -163.8721669 7.583068
## mean_cpss 0.1809726 19.04427 -38.1935432 37.100979
## mean_epsd -43.1105983 19.72568 -81.7401069 -3.945129
## male 175.7927296 32.90762 110.3357974 239.4477624.3.3 Interactions
Next, all of the interactions between exposures or between exposures and covariates
npb.sum2$interactions## Posterior Mean SD 95% CI Lower 95% CI Upper PIP
## [1,] 1.51232500652 9.77946055 0.0000 22.15511 0.0280
## [2,] 0.65433959400 6.19129299 0.0000 0.00000 0.0168
## [3,] -0.00326218467 0.42473806 0.0000 0.00000 0.0020
## [4,] -0.00698232110 0.20080980 0.0000 0.00000 0.0044
## [5,] -0.00258271102 0.46337225 0.0000 0.00000 0.0032
## [6,] -0.01465786232 0.37900692 0.0000 0.00000 0.0028
## [7,] -0.00076245021 0.24923364 0.0000 0.00000 0.0020
## [8,] -0.01720915634 0.58394565 0.0000 0.00000 0.0024
## [9,] 0.00051688821 0.18588148 0.0000 0.00000 0.0024
## [10,] -0.00413202603 0.27656153 0.0000 0.00000 0.0028
## [11,] -0.02641565249 0.83446506 0.0000 0.00000 0.0040
## [12,] -0.00201949522 0.20727279 0.0000 0.00000 0.0016
## [13,] -0.01572387134 0.43302019 0.0000 0.00000 0.0044
## [14,] -0.03420576925 0.93587891 0.0000 0.00000 0.0040
## [15,] -0.00887746095 0.38409965 0.0000 0.00000 0.0016
## [16,] -0.02717263934 0.84536743 0.0000 0.00000 0.0052
## [17,] -0.00915469747 0.31542677 0.0000 0.00000 0.0016
## [18,] -0.05213203027 1.21569385 0.0000 0.00000 0.0044
## [19,] -0.01989527242 0.53419496 0.0000 0.00000 0.0032
## [20,] 0.00265653965 0.34603287 0.0000 0.00000 0.0040
## [21,] -162.01330438843 30.03114028 -242.3003 -117.79902 1.0000
## [22,] -0.01184325393 0.51146950 0.0000 0.00000 0.0036
## [23,] -0.01581913441 0.40541897 0.0000 0.00000 0.0044
## [24,] -0.00175063397 0.12828228 0.0000 0.00000 0.0024
## [25,] -0.06190253022 1.13458263 0.0000 0.00000 0.0052
## [26,] -0.01826842294 0.42458788 0.0000 0.00000 0.0024
## [27,] -0.06284083126 1.26441921 0.0000 0.00000 0.0048
## [28,] -0.01405008554 0.45123778 0.0000 0.00000 0.0044
## [29,] -0.01392133355 0.58023036 0.0000 0.00000 0.0060
## [30,] -0.03418771444 0.82919139 0.0000 0.00000 0.0064
## [31,] -0.00195478053 0.27756505 0.0000 0.00000 0.0028
## [32,] -0.01533309382 0.34615416 0.0000 0.00000 0.0036
## [33,] -0.00246924398 0.39391033 0.0000 0.00000 0.0020
## [34,] -0.00077100846 0.32513796 0.0000 0.00000 0.0036
## [35,] 0.03361347817 0.98484019 0.0000 0.00000 0.0032
## [36,] -0.00263500578 0.44359110 0.0000 0.00000 0.0036
## [37,] -0.00772861063 0.21683726 0.0000 0.00000 0.0028
## [38,] 0.03076925176 1.01178640 0.0000 0.00000 0.0048
## [39,] -0.00636780945 0.21659277 0.0000 0.00000 0.0024
## [40,] -0.00870161813 0.24276099 0.0000 0.00000 0.0032
## [41,] -0.00237384931 0.39054599 0.0000 0.00000 0.0028
## [42,] -0.01033005846 0.46109399 0.0000 0.00000 0.0024
## [43,] -0.00865241668 0.39733920 0.0000 0.00000 0.0016
## [44,] -0.01836745693 0.50492526 0.0000 0.00000 0.0028
## [45,] -0.04265413398 0.99815333 0.0000 0.00000 0.0056
## [46,] -0.01578110771 0.34818414 0.0000 0.00000 0.0040
## [47,] -0.06662207191 1.17559537 0.0000 0.00000 0.0064
## [48,] -0.01948388433 0.53321135 0.0000 0.00000 0.0036
## [49,] 0.01931485945 1.08014670 0.0000 0.00000 0.0040
## [50,] -0.00847375822 0.36105790 0.0000 0.00000 0.0032
## [51,] -0.04065556367 0.84588285 0.0000 0.00000 0.0040
## [52,] 0.00081360093 0.23351018 0.0000 0.00000 0.0036
## [53,] 0.00330232150 0.31501878 0.0000 0.00000 0.0024
## [54,] 0.00215118747 0.28332544 0.0000 0.00000 0.0016
## [55,] -0.02386347007 0.63630564 0.0000 0.00000 0.0028
## [56,] 0.00888292132 0.58780776 0.0000 0.00000 0.0028
## [57,] 0.00516728824 0.50140297 0.0000 0.00000 0.0036
## [58,] 0.00680777122 0.34714313 0.0000 0.00000 0.0032
## [59,] -0.01113713531 0.47136232 0.0000 0.00000 0.0032
## [60,] -0.00428069893 0.48079407 0.0000 0.00000 0.0028
## [61,] -0.00181055679 0.19579166 0.0000 0.00000 0.0036
## [62,] -0.00929964925 0.39727476 0.0000 0.00000 0.0036
## [63,] -0.00076246961 0.24012954 0.0000 0.00000 0.0012
## [64,] -0.01399946919 0.43425929 0.0000 0.00000 0.0044
## [65,] -0.01834968197 0.60942497 0.0000 0.00000 0.0024
## [66,] -0.01676568762 0.45907003 0.0000 0.00000 0.0024
## [67,] 0.00873250723 0.35072876 0.0000 0.00000 0.0032
## [68,] -0.03112746884 0.58896286 0.0000 0.00000 0.0040
## [69,] -0.00916907282 0.26212941 0.0000 0.00000 0.0048
## [70,] -0.00274249181 0.28049818 0.0000 0.00000 0.0024
## [71,] -0.00664142171 0.28458463 0.0000 0.00000 0.0028
## [72,] -0.00148415588 0.49367543 0.0000 0.00000 0.0040
## [73,] -0.00643607825 0.14760824 0.0000 0.00000 0.0020
## [74,] 0.00377571198 0.26397622 0.0000 0.00000 0.0016
## [75,] 0.02172002175 0.94570698 0.0000 0.00000 0.0028
## [76,] 0.00262002602 0.26316336 0.0000 0.00000 0.0016
## [77,] -0.00266481974 0.14267675 0.0000 0.00000 0.0012
## [78,] -0.00931016756 0.32417618 0.0000 0.00000 0.0024
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## [639,] -0.01664597928 0.50535990 0.0000 0.00000 0.0060
## [640,] -0.02634663289 0.56193027 0.0000 0.00000 0.0048
## [641,] -0.00905324719 0.42045398 0.0000 0.00000 0.0052
## [642,] -0.00846997663 0.74586804 0.0000 0.00000 0.0032
## [643,] -0.00697977824 0.33210343 0.0000 0.00000 0.0028
## [644,] -0.19601449582 5.07965513 0.0000 0.00000 0.0048
## [645,] -0.00165916235 0.32875539 0.0000 0.00000 0.0048
## [646,] -0.27687138686 5.56706303 0.0000 0.00000 0.0080
## [647,] -0.00790607460 0.21719232 0.0000 0.00000 0.0024
## [648,] 0.00220809274 0.55195592 0.0000 0.00000 0.0040
## [649,] 0.00486925544 0.34839125 0.0000 0.00000 0.0036
## [650,] -0.00462845550 0.32010838 0.0000 0.00000 0.0020
## [651,] -0.00521275018 0.16915243 0.0000 0.00000 0.0020
## [652,] -0.03140453282 0.93119953 0.0000 0.00000 0.0028
## [653,] 0.00381181407 0.21260252 0.0000 0.00000 0.0008
## [654,] -0.02592653809 0.59060945 0.0000 0.00000 0.0044
## [655,] -0.01811238025 0.66997062 0.0000 0.00000 0.0036
## [656,] -0.01019049691 0.39956909 0.0000 0.00000 0.0028
## [657,] 0.01579965009 1.31401020 0.0000 0.00000 0.0040
## [658,] -0.10741662597 4.37757491 0.0000 0.00000 0.0040
## [659,] -0.12020088607 3.69001858 0.0000 0.00000 0.0024
## [660,] -0.00529449306 0.25263108 0.0000 0.00000 0.0032
## [661,] -0.03623419293 1.23218225 0.0000 0.00000 0.0028
## [662,] -0.80304827285 10.31142488 0.0000 0.00000 0.0084
## [663,] -0.36665734707 6.96915918 0.0000 0.00000 0.0072
## [664,] 0.00089479405 0.60153488 0.0000 0.00000 0.0032
## [665,] 0.00318168175 0.50027252 0.0000 0.00000 0.0028
## [666,] -0.02178480035 0.58246623 0.0000 0.00000 0.0044
## [667,] -0.00798472201 0.35787986 0.0000 0.00000 0.0016
## [668,] -0.18045180228 3.63743561 0.0000 0.00000 0.0064
## [669,] 0.00690934886 0.45148791 0.0000 0.00000 0.0032
## [670,] -0.15319054144 2.53403193 0.0000 0.00000 0.0072
## [671,] -0.02385689138 0.88873503 0.0000 0.00000 0.0020
## [672,] -0.01374904597 0.52279597 0.0000 0.00000 0.0028
## [673,] -0.00575106273 0.39720587 0.0000 0.00000 0.0048
## [674,] -0.29458109077 5.86194441 0.0000 0.00000 0.0064
## [675,] -0.04503259346 0.87201354 0.0000 0.00000 0.0044
## [676,] -0.00542199546 0.27467683 0.0000 0.00000 0.0016
## [677,] -0.01067440578 0.25157526 0.0000 0.00000 0.0024
## [678,] -0.27525068086 4.72668606 0.0000 0.00000 0.0072
## [679,] -0.00152820187 0.27963285 0.0000 0.00000 0.0020
## [680,] -0.06602514049 1.70130620 0.0000 0.00000 0.0056
## [681,] 0.02908860103 1.08433178 0.0000 0.00000 0.0016
## [682,] 0.01689078693 1.46996297 0.0000 0.00000 0.0032
## [683,] -0.00581012623 0.25055465 0.0000 0.00000 0.0032
## [684,] -0.02021446488 0.46104437 0.0000 0.00000 0.0044
## [685,] -0.07116631254 2.35218504 0.0000 0.00000 0.0048
## [686,] -0.02720137318 0.95292982 0.0000 0.00000 0.0052
## [687,] -0.01667264217 0.51533834 0.0000 0.00000 0.0040
## [688,] -0.01919501060 0.84899793 0.0000 0.00000 0.0044
## [689,] -0.61029405909 9.59225940 0.0000 0.00000 0.0076
## [690,] -0.07287090867 1.89400144 0.0000 0.00000 0.0048
## [691,] 0.03117001282 1.75713325 0.0000 0.00000 0.0016
## [692,] -0.09945375428 2.51140400 0.0000 0.00000 0.0048
## [693,] -0.01487130862 0.50732573 0.0000 0.00000 0.0040
## [694,] 0.02016369622 1.48900965 0.0000 0.00000 0.0024
## [695,] 0.07853813440 2.87095205 0.0000 0.00000 0.0056
## [696,] -0.07986366102 2.91589908 0.0000 0.00000 0.0064
## [697,] 0.08490171280 2.64061809 0.0000 0.00000 0.0036
## [698,] -0.05899234853 2.16326746 0.0000 0.00000 0.0036
## [699,] -0.00329126955 0.23356264 0.0000 0.00000 0.0020
## [700,] -0.27534672630 6.56685696 0.0000 0.00000 0.0052
## [701,] -0.00806030018 0.34443363 0.0000 0.00000 0.0028
## [702,] -0.01013860162 0.78816363 0.0000 0.00000 0.0040
## [703,] -0.02143911209 0.44654366 0.0000 0.00000 0.0040
## [704,] -0.02669023315 0.77350618 0.0000 0.00000 0.0040
## [705,] 0.04141267459 1.54081181 0.0000 0.00000 0.0032
## [706,] 0.00226294831 0.35445201 0.0000 0.00000 0.0044
## [707,] -0.03303268348 0.84476512 0.0000 0.00000 0.0048
## [708,] -0.01160823315 0.56099623 0.0000 0.00000 0.0040
## [709,] -0.00635494262 0.35944750 0.0000 0.00000 0.0036
## [710,] 0.04520069231 3.30998920 0.0000 0.00000 0.0052
## [711,] -0.01777173315 0.68990287 0.0000 0.00000 0.0024
## [712,] -0.02189853965 0.60907811 0.0000 0.00000 0.0032
## [713,] -0.03278246162 1.08868488 0.0000 0.00000 0.0040
## [714,] -0.04646872397 1.37795145 0.0000 0.00000 0.0044
## [715,] -0.97633663142 12.13436899 0.0000 0.00000 0.0096
## [716,] 0.00041403376 0.96440102 0.0000 0.00000 0.0040
## [717,] -0.00243589264 0.55716014 0.0000 0.00000 0.0028
## [718,] -0.03140013911 0.62951857 0.0000 0.00000 0.0032
## [719,] -0.02553283917 0.62318065 0.0000 0.00000 0.0032
## [720,] -0.05622686401 1.71438085 0.0000 0.00000 0.0052
## [721,] -0.01284337506 1.84060116 0.0000 0.00000 0.0052
## [722,] -0.02769424852 0.76660660 0.0000 0.00000 0.0040
## [723,] 0.47022087004 6.59906072 0.0000 0.00000 0.0092
## [724,] -0.01109527792 0.62473872 0.0000 0.00000 0.0028
## [725,] -0.01635231371 0.51039839 0.0000 0.00000 0.0048
## [726,] -0.01575908862 0.79925866 0.0000 0.00000 0.0044
## [727,] -0.00706276861 0.20749028 0.0000 0.00000 0.0028
## [728,] -0.03442170712 0.71864012 0.0000 0.00000 0.0044
## [729,] -0.01996918928 0.63925587 0.0000 0.00000 0.0048
## [730,] -0.06906748911 1.80453514 0.0000 0.00000 0.0052
## [731,] -0.00812970724 0.42756813 0.0000 0.00000 0.0044
## [732,] -0.03990865497 1.01934928 0.0000 0.00000 0.0028
## [733,] -0.01613020637 0.64276676 0.0000 0.00000 0.0044
## [734,] 0.00463493246 0.57770717 0.0000 0.00000 0.0020
## [735,] 0.05425932404 2.52405836 0.0000 0.00000 0.0028
## [736,] -0.02137925793 1.27743333 0.0000 0.00000 0.0032
## [737,] -0.11636730244 4.25156934 0.0000 0.00000 0.0052
## [738,] -0.00933582507 0.36424341 0.0000 0.00000 0.0048
## [739,] -0.01689753800 0.38393045 0.0000 0.00000 0.0032
## [740,] -0.01496408271 0.27598012 0.0000 0.00000 0.0040
## [741,] 0.01212822901 3.99332700 0.0000 0.00000 0.0044
## [742,] 0.01414875155 0.87022017 0.0000 0.00000 0.0036
## [743,] -0.01892256195 0.63632012 0.0000 0.00000 0.0016
## [744,] -0.01759978179 1.08441120 0.0000 0.00000 0.0040
## [745,] 0.03557865145 1.35222242 0.0000 0.00000 0.0044
## [746,] -0.04372623547 1.04865325 0.0000 0.00000 0.0048
## [747,] 0.02213702164 1.68815240 0.0000 0.00000 0.0040
## [748,] -0.94371972114 11.14448282 0.0000 0.00000 0.0112
## [749,] 1.79459201349 13.85952633 0.0000 0.00000 0.0212
## [750,] -0.02946964620 0.82575788 0.0000 0.00000 0.0036
## [751,] 0.00177158701 0.27312243 0.0000 0.00000 0.0044
## [752,] -0.08542823113 3.20990084 0.0000 0.00000 0.0020
## [753,] -0.00777424026 0.48163682 0.0000 0.00000 0.0032
## [754,] -0.01135251454 0.35147502 0.0000 0.00000 0.0040
## [755,] 0.00229807127 0.13340158 0.0000 0.00000 0.0016
## [756,] -0.00435365163 0.11300572 0.0000 0.00000 0.00244.3.4 Predict fitted values for each individual
pred.npb2 <- predict(fit.npb2)
fittedvals2 <- pred.npb2$fitted.vals4.3.5 Plot predicted outcomes against “measured” outcomes
plot(fittedvals2, Y)
abline(a = 0, b = 1, col = "red")
4.4 Fit the NPB model without ozone and with temperature
Only ozone shows up in the NPB model. However, there is some speculation that ozone is just a proxy for some of the other variables. Here I am running the NPB model without ozone but with temperature just to see if something else pops up instead.
priors.npb <- priors.npb.24
#' Exposures
colnames(X.scaled)## [1] "mean_pm" "mean_o3" "mean_temp"
## [4] "pct_tree_cover" "pct_impervious" "mean_aadt_intensity"
## [7] "dist_m_tri" "dist_m_npl" "dist_m_waste_site"
## [10] "dist_m_major_emit" "dist_m_cafo" "dist_m_mine_well"
## [13] "cvd_rate_adj" "res_rate_adj" "violent_crime_rate"
## [16] "property_crime_rate" "pct_less_hs" "pct_unemp"
## [19] "pct_limited_eng" "pct_hh_pov" "pct_poc"#' Covariates
colnames(W.scaled2)## [1] "lat" "lon" "lat_lon_int" "latina_re"
## [5] "black_re" "other_re" "ed_no_hs" "ed_hs"
## [9] "ed_aa" "ed_4yr" "low_bmi" "ovwt_bmi"
## [13] "obese_bmi" "concep_spring" "concep_summer" "concep_fall"
## [17] "concep_2010" "concep_2011" "concep_2012" "concep_2013"
## [21] "maternal_age" "any_smoker" "smokeSH" "mean_cpss"
## [25] "mean_epsd" "male"# fit.npb3 <- npb(niter = 5000, nburn = 2500, X = X.scaled[,-c(2)], Y = Y, W = W.scaled2,
# scaleY = TRUE,
# priors = priors.npb, interact = TRUE, XWinteract = TRUE)
# save(fit.npb3, file = here::here("Results", "NPB_Birth_Weight_v4.3.rdata"))
load(here::here("Results", "NPB_Birth_Weight_v4.3.rdata"))
npb.sum3 <- summary(fit.npb3)4.4.1 First, main effect regression coefficients with PIPs
rownames(npb.sum3$main.effects) <- colnames(X.scaled[,-c(2)])
npb.sum3$main.effects## Posterior Mean SD 95% CI Lower 95% CI Upper PIP
## mean_pm -5.0812657 11.389288 -38.420777 4.123733 0.4308
## mean_temp -4.3626863 13.839561 -38.100412 7.899612 0.4064
## pct_tree_cover -1.0942565 5.378364 -14.926393 8.862679 0.2992
## pct_impervious -1.6628395 5.689727 -17.895070 5.520513 0.3044
## mean_aadt_intensity -0.1461904 5.585696 -10.742507 12.956853 0.2856
## dist_m_tri -1.0196214 5.847048 -15.541244 10.630242 0.3096
## dist_m_npl -0.5963490 4.986723 -12.544201 10.099711 0.2736
## dist_m_waste_site 1.7286714 9.421148 -9.610017 32.957196 0.3028
## dist_m_major_emit 0.3675718 6.164625 -9.898133 15.820179 0.2704
## dist_m_cafo -1.9038253 12.951734 -26.013467 12.491398 0.3528
## dist_m_mine_well -3.4827117 9.222471 -31.808167 6.997606 0.3928
## cvd_rate_adj -2.1767251 6.695723 -21.070834 5.664834 0.3408
## res_rate_adj -3.1881258 8.110302 -28.146459 3.997973 0.3732
## violent_crime_rate -0.5876895 6.508686 -14.093171 11.614945 0.2952
## property_crime_rate -2.0397891 6.325035 -21.728442 5.620994 0.3164
## pct_less_hs -1.8967882 7.213950 -22.183937 7.013704 0.3464
## pct_unemp -5.8335999 12.030417 -44.665861 1.948495 0.4236
## pct_limited_eng -1.5263159 5.896443 -18.006636 5.145165 0.3028
## pct_hh_pov -1.0088890 5.682389 -13.882495 8.026244 0.2944
## pct_poc -1.2612110 6.168611 -15.669226 8.062277 0.30884.4.2 Next, posterior means and CIs for covariates
rownames(npb.sum3$covariates)[2:nrow(npb.sum3$covariates)] <- colnames(W.scaled2)
npb.sum3$covariates## Posterior Mean SD 95% CI Lower 95% CI Upper
## <NA> 3098.1638005 220.55767 2666.16731 3521.023986
## lat -3.7627440 316.24845 -591.88631 640.998702
## lon 17.5273433 150.50755 -288.88048 302.966289
## lat_lon_int 6.6346924 382.01299 -706.38282 780.957835
## latina_re -86.9586612 46.73207 -178.34704 3.203535
## black_re -266.2797304 50.54625 -365.94085 -171.826949
## other_re -69.3997914 67.37664 -202.46007 60.171943
## ed_no_hs 179.8146814 76.85391 26.64261 332.454757
## ed_hs 148.1126396 68.46618 13.87560 280.296072
## ed_aa 89.1501583 60.79692 -31.19665 206.845061
## ed_4yr 81.9459821 50.90430 -16.21741 184.391578
## low_bmi -60.5779496 87.36124 -236.61667 108.064368
## ovwt_bmi 43.8939494 39.74888 -33.12864 127.562779
## obese_bmi 104.1161638 44.98080 15.72703 189.126295
## concep_spring 318.8454440 79.41647 159.09605 465.836976
## concep_summer 47.3579197 49.24591 -58.91000 139.801592
## concep_fall 336.5041638 71.77026 192.17841 477.136186
## concep_2010 8.8457287 218.76118 -414.06074 423.202185
## concep_2011 -52.0586515 218.00509 -470.98222 370.977430
## concep_2012 0.7873579 216.77994 -419.12965 416.732783
## concep_2013 54.9375621 216.83024 -364.59266 472.761783
## maternal_age 68.8376962 21.53227 27.87594 112.920432
## any_smoker -121.0587273 62.57526 -244.01512 -2.580118
## smokeSH -105.5301323 44.40938 -190.21874 -18.568521
## mean_cpss 7.7903273 19.18910 -29.30275 45.910796
## mean_epsd -44.6502069 19.70121 -81.02006 -6.056464
## male 170.2833195 32.06464 110.41655 232.4006604.4.3 Interactions
Next, all of the interactions between exposures or between exposures and covariates
npb.sum3$interactions## Posterior Mean SD 95% CI Lower 95% CI Upper PIP
## [1,] -0.002769623604 0.198664905 0.0000 0.0000 0.0012
## [2,] 0.002676103140 0.226259859 0.0000 0.0000 0.0008
## [3,] -0.017689095548 0.454321419 0.0000 0.0000 0.0016
## [4,] 0.022607066757 0.706450372 0.0000 0.0000 0.0016
## [5,] -0.004815508237 0.454880039 0.0000 0.0000 0.0008
## [6,] -0.003618262125 0.207005072 0.0000 0.0000 0.0012
## [7,] -0.010175297406 0.470189316 0.0000 0.0000 0.0024
## [8,] -0.006493587924 0.246554838 0.0000 0.0000 0.0016
## [9,] -0.010169208510 0.324262064 0.0000 0.0000 0.0012
## [10,] -0.006256413501 0.216784895 0.0000 0.0000 0.0016
## [11,] 0.000075906071 0.254461017 0.0000 0.0000 0.0016
## [12,] -0.002315005571 0.115750279 0.0000 0.0000 0.0004
## [13,] -0.001431785327 0.315273728 0.0000 0.0000 0.0024
## [14,] 0.000000000000 0.000000000 0.0000 0.0000 0.0000
## [15,] 0.000207662552 0.010383128 0.0000 0.0000 0.0004
## [16,] -0.002920286744 0.146014337 0.0000 0.0000 0.0004
## [17,] -0.005366736115 0.268336806 0.0000 0.0000 0.0004
## [18,] -0.019314605808 0.604048841 0.0000 0.0000 0.0016
## [19,] 0.000000000000 0.000000000 0.0000 0.0000 0.0000
## [20,] -0.014699578938 0.403945782 0.0000 0.0000 0.0020
## [21,] 0.002207182138 0.328897169 0.0000 0.0000 0.0016
## [22,] -0.012640978532 0.439895464 0.0000 0.0000 0.0012
## [23,] -0.037838205015 0.801984518 0.0000 0.0000 0.0032
## [24,] -0.002452025727 0.231625135 0.0000 0.0000 0.0012
## [25,] -0.006340093628 0.306499632 0.0000 0.0000 0.0012
## [26,] -0.003825092245 0.537817746 0.0000 0.0000 0.0012
## [27,] -0.028016195737 0.835301220 0.0000 0.0000 0.0024
## [28,] -0.006770226758 0.259096849 0.0000 0.0000 0.0008
## [29,] -0.005833794573 0.195134526 0.0000 0.0000 0.0012
## [30,] -0.003382051342 0.172974543 0.0000 0.0000 0.0008
## [31,] -0.019817398383 0.667056390 0.0000 0.0000 0.0012
## [32,] -0.000485441096 0.024272055 0.0000 0.0000 0.0004
## [33,] 0.002785191465 0.152715661 0.0000 0.0000 0.0016
## [34,] 0.002619637285 0.364446135 0.0000 0.0000 0.0016
## [35,] 0.002892476028 0.338203520 0.0000 0.0000 0.0016
## [36,] 0.004819809569 0.273732352 0.0000 0.0000 0.0012
## [37,] 0.002825693695 0.314887061 0.0000 0.0000 0.0012
## [38,] 0.000648084403 0.032404220 0.0000 0.0000 0.0004
## [39,] 0.004200631152 0.359057907 0.0000 0.0000 0.0008
## [40,] -0.002348263080 0.134685014 0.0000 0.0000 0.0012
## [41,] 0.000000000000 0.000000000 0.0000 0.0000 0.0000
## [42,] -0.007539389382 0.245251653 0.0000 0.0000 0.0024
## [43,] 0.030311034884 1.000450173 0.0000 0.0000 0.0012
## [44,] -0.001030528481 0.150591214 0.0000 0.0000 0.0008
## [45,] -0.009494168271 0.393523172 0.0000 0.0000 0.0008
## [46,] 0.000450137268 0.384231330 0.0000 0.0000 0.0012
## [47,] -0.008536496303 0.435130695 0.0000 0.0000 0.0016
## [48,] -0.013952811051 0.450805324 0.0000 0.0000 0.0020
## [49,] -0.003586128585 0.138081806 0.0000 0.0000 0.0008
## [50,] -0.008938348458 0.311250524 0.0000 0.0000 0.0020
## [51,] -0.006595719891 0.202351834 0.0000 0.0000 0.0016
## [52,] 0.000000000000 0.000000000 0.0000 0.0000 0.0000
## [53,] 0.000000000000 0.000000000 0.0000 0.0000 0.0000
## [54,] -0.023124765682 0.711427982 0.0000 0.0000 0.0020
## [55,] 0.004256201627 0.376006383 0.0000 0.0000 0.0024
## [56,] -0.000086827426 0.238246181 0.0000 0.0000 0.0020
## [57,] 0.000422048717 0.021102436 0.0000 0.0000 0.0004
## [58,] -0.000196335845 0.009816792 0.0000 0.0000 0.0004
## [59,] -0.000939553726 0.046977686 0.0000 0.0000 0.0004
## [60,] -0.008883954457 0.314042246 0.0000 0.0000 0.0008
## [61,] 0.005385011084 0.269250554 0.0000 0.0000 0.0004
## [62,] -0.050241440971 1.077723283 0.0000 0.0000 0.0032
## [63,] -0.002271831586 0.155904862 0.0000 0.0000 0.0012
## [64,] -0.004324079959 0.158515992 0.0000 0.0000 0.0008
## [65,] -0.005549417512 0.196710517 0.0000 0.0000 0.0008
## [66,] -0.009435258517 0.413831614 0.0000 0.0000 0.0008
## [67,] 0.000000000000 0.000000000 0.0000 0.0000 0.0000
## [68,] -0.015479638368 0.612589501 0.0000 0.0000 0.0024
## [69,] 0.000000000000 0.000000000 0.0000 0.0000 0.0000
## [70,] -0.004799254986 0.239962749 0.0000 0.0000 0.0004
## [71,] 0.009534850957 0.488029163 0.0000 0.0000 0.0008
## [72,] -0.000370767004 0.482264779 0.0000 0.0000 0.0016
## [73,] 0.004766936626 0.322944110 0.0000 0.0000 0.0020
## [74,] -0.004026562566 0.128292250 0.0000 0.0000 0.0012
## [75,] -0.008634181121 0.266856544 0.0000 0.0000 0.0012
## [76,] 0.001172309950 0.109324693 0.0000 0.0000 0.0008
## [77,] -0.016923851571 0.406257633 0.0000 0.0000 0.0020
## [78,] -0.011278818285 0.305233323 0.0000 0.0000 0.0016
## [79,] -0.000346309058 0.017315453 0.0000 0.0000 0.0004
## [80,] -0.001816860159 0.153133347 0.0000 0.0000 0.0012
## [81,] -0.000332692986 0.035777847 0.0000 0.0000 0.0012
## [82,] -0.001153712032 0.194481961 0.0000 0.0000 0.0012
## [83,] 0.006479901384 0.329735569 0.0000 0.0000 0.0016
## [84,] -0.003525837893 0.176291895 0.0000 0.0000 0.0004
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## [638,] -0.008099647451 0.242356246 0.0000 0.0000 0.0012
## [639,] -0.022516922347 0.941866831 0.0000 0.0000 0.0020
## [640,] -0.005430692422 0.480274828 0.0000 0.0000 0.0016
## [641,] -0.001599923391 0.065021754 0.0000 0.0000 0.0008
## [642,] -0.005306290406 0.188517318 0.0000 0.0000 0.0008
## [643,] -0.006616600927 0.330830046 0.0000 0.0000 0.0004
## [644,] 0.006615043121 0.303179134 0.0000 0.0000 0.0008
## [645,] -0.012322193010 0.518641820 0.0000 0.0000 0.0012
## [646,] -0.006538030447 0.187061449 0.0000 0.0000 0.0016
## [647,] 0.005520128318 0.363010478 0.0000 0.0000 0.0008
## [648,] -0.015227851631 0.466903004 0.0000 0.0000 0.0016
## [649,] 0.028395625035 1.444266989 0.0000 0.0000 0.0008
## [650,] -0.042718835626 1.125787316 0.0000 0.0000 0.0020
## [651,] 0.162892456930 3.469162025 0.0000 0.0000 0.0040
## [652,] -0.000655872685 0.159191479 0.0000 0.0000 0.0016
## [653,] -0.004906092198 0.295956188 0.0000 0.0000 0.0016
## [654,] -0.029347964213 1.336092126 0.0000 0.0000 0.0012
## [655,] -0.009509074531 0.292699455 0.0000 0.0000 0.0012
## [656,] -0.005166752942 0.466258277 0.0000 0.0000 0.0012
## [657,] -0.006114190351 0.218730160 0.0000 0.0000 0.0008
## [658,] -0.022986478062 1.058483007 0.0000 0.0000 0.0024
## [659,] -0.011764487099 0.449341408 0.0000 0.0000 0.0016
## [660,] -0.023032464802 0.686177804 0.0000 0.0000 0.0020
## [661,] 0.002466843473 0.287069455 0.0000 0.0000 0.0016
## [662,] 0.000008702562 0.169200856 0.0000 0.0000 0.0012
## [663,] -0.003415979545 0.221966700 0.0000 0.0000 0.0020
## [664,] 0.023147800001 0.969673792 0.0000 0.0000 0.0016
## [665,] -0.013242589085 0.638309333 0.0000 0.0000 0.0008
## [666,] 0.000002008863 0.316003899 0.0000 0.0000 0.0020
## [667,] -0.003834899791 0.143457256 0.0000 0.0000 0.0008
## [668,] -0.000223093125 0.011154656 0.0000 0.0000 0.0004
## [669,] -0.050083584311 2.763603187 0.0000 0.0000 0.0012
## [670,] -0.021807779019 0.528047733 0.0000 0.0000 0.0020
## [671,] -0.013885269152 0.639313910 0.0000 0.0000 0.0012
## [672,] 0.001847485713 1.731376575 0.0000 0.0000 0.0024
## [673,] -0.010078820283 0.315505506 0.0000 0.0000 0.0016
## [674,] -0.010346180338 0.427532359 0.0000 0.0000 0.0016
## [675,] -0.000959532906 0.297550668 0.0000 0.0000 0.0020
## [676,] -0.007742644433 0.377518875 0.0000 0.0000 0.0016
## [677,] 0.458147979187 6.849257000 0.0000 0.0000 0.0056
## [678,] -0.018840079189 0.533092295 0.0000 0.0000 0.0020
## [679,] -0.002567198771 0.128359939 0.0000 0.0000 0.0004
## [680,] -0.005148509824 0.448626421 0.0000 0.0000 0.0008
## [681,] -0.008891793505 0.253808903 0.0000 0.0000 0.0020
## [682,] -0.000036508456 0.176901169 0.0000 0.0000 0.0012
## [683,] -0.015118982838 0.755949142 0.0000 0.0000 0.0004
## [684,] -0.020869835882 0.607293670 0.0000 0.0000 0.0020
## [685,] 0.001141787604 0.359977158 0.0000 0.0000 0.0012
## [686,] -0.015991858798 0.563425781 0.0000 0.0000 0.0016
## [687,] -0.000550617721 0.163257863 0.0000 0.0000 0.0008
## [688,] -0.010146534393 0.342032377 0.0000 0.0000 0.0016
## [689,] -0.011581824963 0.579091248 0.0000 0.0000 0.0004
## [690,] -0.022256794441 0.633628698 0.0000 0.0000 0.0016
## [691,] -0.003750842577 0.351227021 0.0000 0.0000 0.0016
## [692,] 0.000000000000 0.000000000 0.0000 0.0000 0.0000
## [693,] -0.004910211972 0.250846461 0.0000 0.0000 0.0024
## [694,] -0.004270543288 0.154016171 0.0000 0.0000 0.0008
## [695,] -0.008473216475 0.315276715 0.0000 0.0000 0.0012
## [696,] -0.010404344443 0.496529060 0.0000 0.0000 0.0008
## [697,] -0.005884076542 0.294203827 0.0000 0.0000 0.0004
## [698,] -0.012668341643 0.735272199 0.0000 0.0000 0.0016
## [699,] 0.030471096026 1.625674083 0.0000 0.0000 0.0008
## [700,] -0.008879136980 0.836524582 0.0000 0.0000 0.0024
## [701,] 0.014651838059 0.795334575 0.0000 0.0000 0.0012
## [702,] -0.079998999029 2.515463052 0.0000 0.0000 0.0020
## [703,] 1.649691275482 13.065987190 0.0000 0.0000 0.0188
## [704,] -0.014540488584 1.046134987 0.0000 0.0000 0.0024
## [705,] -0.006903006355 0.298562290 0.0000 0.0000 0.0008
## [706,] -0.004135288899 0.150384461 0.0000 0.0000 0.0008
## [707,] 0.063585429958 1.610385562 0.0000 0.0000 0.0020
## [708,] -0.039278016278 0.950504640 0.0000 0.0000 0.0028
## [709,] -0.002925792351 0.385587234 0.0000 0.0000 0.0020
## [710,] -0.007347582265 0.276866945 0.0000 0.0000 0.00124.4.4 Predict fitted values for each individual
pred.npb3 <- predict(fit.npb3)
fittedvals3 <- pred.npb3$fitted.vals4.4.5 Plot predicted outcomes against “measured” outcomes
plot(fittedvals3, Y)
abline(a = 0, b = 1, col = "red")
4.5 Fit the NPB model without ozone and without temperature
Only ozone shows up in the NPB model. However, there is some speculation that ozone is just a proxy for some of the other variables. Here I am running the NPB model without ozone or temperature just to see if something else pops up instead.
priors.npb <- priors.npb.24
#' Exposures
colnames(X.scaled)## [1] "mean_pm" "mean_o3" "mean_temp"
## [4] "pct_tree_cover" "pct_impervious" "mean_aadt_intensity"
## [7] "dist_m_tri" "dist_m_npl" "dist_m_waste_site"
## [10] "dist_m_major_emit" "dist_m_cafo" "dist_m_mine_well"
## [13] "cvd_rate_adj" "res_rate_adj" "violent_crime_rate"
## [16] "property_crime_rate" "pct_less_hs" "pct_unemp"
## [19] "pct_limited_eng" "pct_hh_pov" "pct_poc"#' Covariates
colnames(W.scaled2)## [1] "lat" "lon" "lat_lon_int" "latina_re"
## [5] "black_re" "other_re" "ed_no_hs" "ed_hs"
## [9] "ed_aa" "ed_4yr" "low_bmi" "ovwt_bmi"
## [13] "obese_bmi" "concep_spring" "concep_summer" "concep_fall"
## [17] "concep_2010" "concep_2011" "concep_2012" "concep_2013"
## [21] "maternal_age" "any_smoker" "smokeSH" "mean_cpss"
## [25] "mean_epsd" "male"# fit.npb4 <- npb(niter = 5000, nburn = 2500, X = X.scaled[,-c(2,3)], Y = Y, W = W.scaled2,
# scaleY = TRUE,
# priors = priors.npb, interact = TRUE, XWinteract = TRUE)
# save(fit.npb4, file = here::here("Results", "NPB_Birth_Weight_v4.4.rdata"))
load(here::here("Results", "NPB_Birth_Weight_v4.4.rdata"))
npb.sum4 <- summary(fit.npb4)4.5.1 First, main effect regression coefficients with PIPs
rownames(npb.sum4$main.effects) <- colnames(X.scaled[,-c(2,3)])
npb.sum4$main.effects## Posterior Mean SD 95% CI Lower 95% CI Upper PIP
## mean_pm 0.40578368 6.238661 -10.652441 16.447532 0.2812
## pct_tree_cover 0.28421997 5.425274 -10.914631 15.160063 0.2832
## pct_impervious -0.70674846 6.141713 -16.346584 10.648090 0.2796
## mean_aadt_intensity 0.55679440 5.408335 -9.936939 16.097481 0.2692
## dist_m_tri 0.08654166 6.150674 -11.611509 15.084605 0.2744
## dist_m_npl 0.93564634 6.284110 -9.171112 18.764155 0.2744
## dist_m_waste_site 4.16087038 12.119108 -6.881603 43.982400 0.3464
## dist_m_major_emit 0.86835459 5.777090 -8.191580 19.314876 0.2712
## dist_m_cafo -1.33503413 15.246851 -29.651063 17.365238 0.3132
## dist_m_mine_well -1.80077181 8.251401 -26.867929 8.701758 0.3168
## cvd_rate_adj -0.84099481 6.469780 -17.481338 10.128433 0.2792
## res_rate_adj -1.64087938 7.134150 -22.954125 6.281887 0.2880
## violent_crime_rate 0.05864854 5.334227 -10.418866 12.035443 0.2572
## property_crime_rate -1.02677057 5.777023 -15.971722 9.167573 0.2788
## pct_less_hs -0.66943978 6.683276 -17.264286 11.520644 0.2820
## pct_unemp -7.11959173 16.077084 -58.746261 3.884256 0.3960
## pct_limited_eng -0.56072140 5.524495 -13.458147 9.608179 0.2620
## pct_hh_pov -0.42073538 6.302446 -13.637270 10.841550 0.2684
## pct_poc -0.13404666 5.949404 -11.946607 12.252535 0.27804.5.2 Next, posterior means and CIs for covariates
rownames(npb.sum4$covariates)[2:nrow(npb.sum4$covariates)] <- colnames(W.scaled2)
npb.sum4$covariates## Posterior Mean SD 95% CI Lower 95% CI Upper
## <NA> 3120.535218 219.29749 2699.042291 3546.932057
## lat -3.795602 321.43876 -614.074342 629.389403
## lon 19.085662 152.69995 -282.057423 312.470144
## lat_lon_int 3.748911 388.29935 -733.224287 776.084645
## latina_re -96.538265 50.09444 -192.762206 3.319902
## black_re -290.183017 52.88066 -392.740160 -184.533097
## other_re -99.551320 70.94282 -237.665371 33.141455
## ed_no_hs 157.241470 78.73725 2.875724 316.566068
## ed_hs 118.300995 69.66653 -16.340760 253.266877
## ed_aa 67.228957 61.77927 -55.035484 186.529801
## ed_4yr 71.721410 51.21694 -32.133348 169.912563
## low_bmi -100.687523 92.80810 -279.360928 76.766449
## ovwt_bmi 37.235686 40.92351 -43.287059 117.294026
## obese_bmi 106.474291 47.27165 15.650658 197.090196
## concep_spring -45.216744 47.33994 -136.894332 44.267383
## concep_summer 53.816241 47.96052 -39.889655 148.573527
## concep_fall 52.719670 47.07428 -38.781966 144.472922
## concep_2010 18.259475 217.90207 -407.242303 444.323639
## concep_2011 -4.738714 214.18524 -416.690161 396.751064
## concep_2012 -47.411805 215.57707 -465.331351 363.298072
## concep_2013 73.871642 215.61888 -341.464614 487.996479
## maternal_age 67.735252 21.82605 24.596350 109.922671
## any_smoker -128.385180 66.22466 -257.638760 6.282617
## smokeSH -104.347116 44.78335 -190.909975 -16.254499
## mean_cpss 8.552527 19.66978 -30.924747 45.460107
## mean_epsd -51.341508 20.36015 -91.356007 -11.333571
## male 160.851337 32.62179 97.956052 227.2542314.5.3 Interactions
Next, all of the interactions between exposures or between exposures and covariates
npb.sum4$interactions## Posterior Mean SD 95% CI Lower 95% CI Upper PIP
## [1,] -0.02065446795 0.6015368 0 0 0.0056
## [2,] -0.02341076319 0.8228203 0 0 0.0072
## [3,] 0.02485529396 0.7418679 0 0 0.0048
## [4,] -0.01496215309 0.6473938 0 0 0.0080
## [5,] -0.00482031233 0.4670947 0 0 0.0044
## [6,] -0.02469669327 0.6503256 0 0 0.0112
## [7,] -0.05258158697 0.8446635 0 0 0.0100
## [8,] -0.01059384634 0.2747343 0 0 0.0052
## [9,] -0.03631715034 0.7110691 0 0 0.0068
## [10,] -0.00888547190 0.4987186 0 0 0.0072
## [11,] 0.00309019847 0.9441684 0 0 0.0088
## [12,] -0.02612465942 0.5632420 0 0 0.0076
## [13,] -0.02465078038 0.5384283 0 0 0.0084
## [14,] -0.03828614499 1.0866126 0 0 0.0080
## [15,] 0.00137577824 0.4276096 0 0 0.0056
## [16,] -0.07024542069 1.4551794 0 0 0.0088
## [17,] -0.02147735667 0.6241154 0 0 0.0076
## [18,] -0.01496887365 0.5962158 0 0 0.0096
## [19,] 0.00034923212 0.5038999 0 0 0.0068
## [20,] -0.00849113339 0.6176878 0 0 0.0072
## [21,] -0.01644835308 0.3685240 0 0 0.0072
## [22,] 0.00939165483 0.3767220 0 0 0.0048
## [23,] -0.00882311763 0.2478394 0 0 0.0056
## [24,] 0.02350289386 0.8159647 0 0 0.0092
## [25,] -0.02887065157 0.6933436 0 0 0.0056
## [26,] -0.06457714471 1.2314826 0 0 0.0100
## [27,] 0.00484344233 0.3030374 0 0 0.0048
## [28,] -0.01605947641 0.7122592 0 0 0.0068
## [29,] -0.02858913398 0.5816460 0 0 0.0052
## [30,] -0.01756085774 0.4066001 0 0 0.0052
## [31,] -0.02084713198 0.6446724 0 0 0.0044
## [32,] -0.00925948967 0.9450859 0 0 0.0056
## [33,] -0.00423364159 0.4182012 0 0 0.0076
## [34,] 0.03022255470 1.1236425 0 0 0.0080
## [35,] -0.00835636462 0.4274997 0 0 0.0088
## [36,] 0.01401058768 0.7505233 0 0 0.0080
## [37,] 0.03756279610 1.0257230 0 0 0.0080
## [38,] 0.00130939493 0.1646558 0 0 0.0032
## [39,] -0.00233030888 0.8668748 0 0 0.0088
## [40,] -0.02639539710 0.5346244 0 0 0.0084
## [41,] -0.01628525699 0.5438343 0 0 0.0088
## [42,] -0.00592696294 0.2232116 0 0 0.0052
## [43,] -0.00663602300 0.6183788 0 0 0.0068
## [44,] -0.04792206879 0.8730535 0 0 0.0080
## [45,] -0.00922201832 0.4621741 0 0 0.0080
## [46,] -0.01589233420 0.4759240 0 0 0.0068
## [47,] -0.00214994390 0.4088931 0 0 0.0068
## [48,] -0.03141014339 0.6370374 0 0 0.0068
## [49,] -0.00594966491 0.6956222 0 0 0.0076
## [50,] -0.02466581727 0.9043653 0 0 0.0072
## [51,] -0.00595767439 0.3282689 0 0 0.0068
## [52,] 0.05728879704 1.5234056 0 0 0.0092
## [53,] -0.00611425681 0.6199917 0 0 0.0060
## [54,] 0.00997451760 0.4412287 0 0 0.0064
## [55,] 0.06464651684 1.5354598 0 0 0.0092
## [56,] -0.02385158752 0.8825710 0 0 0.0080
## [57,] -0.06318203102 1.2263254 0 0 0.0088
## [58,] -0.03002425122 0.9566229 0 0 0.0092
## [59,] -0.02329722502 0.6443755 0 0 0.0048
## [60,] -0.01840088140 0.4712620 0 0 0.0064
## [61,] -0.01353423412 0.3695652 0 0 0.0084
## [62,] 0.01293726341 0.8087230 0 0 0.0092
## [63,] -0.00084032418 0.8772134 0 0 0.0060
## [64,] -0.02526438827 0.4437155 0 0 0.0112
## [65,] 0.00258408702 0.4313218 0 0 0.0060
## [66,] 0.05193732841 1.0283016 0 0 0.0080
## [67,] -0.00504686581 0.2839564 0 0 0.0080
## [68,] -0.00289700914 0.2015575 0 0 0.0048
## [69,] -0.00233572180 0.5217469 0 0 0.0080
## [70,] 0.00970885728 0.4283611 0 0 0.0072
## [71,] -0.00592771137 0.5287096 0 0 0.0104
## [72,] 0.00512369618 0.2455939 0 0 0.0056
## [73,] -0.00375340316 0.5311847 0 0 0.0068
## [74,] 0.00642854820 0.4920710 0 0 0.0056
## [75,] -0.00134992785 0.6483244 0 0 0.0076
## [76,] -0.00379124546 0.5979684 0 0 0.0080
## [77,] 0.04105058184 1.2356446 0 0 0.0088
## [78,] 0.06316493921 1.9422846 0 0 0.0076
## [79,] 0.00669937989 0.7576487 0 0 0.0084
## [80,] 0.03918544003 0.8717524 0 0 0.0092
## [81,] 0.00490085617 0.5438648 0 0 0.0060
## [82,] 0.01360793143 1.1364362 0 0 0.0084
## [83,] -0.00345789977 0.1706089 0 0 0.0036
## [84,] -0.02034963341 0.9731857 0 0 0.0092
## [85,] 0.00217519726 0.4786369 0 0 0.0056
## [86,] 0.00363870866 0.3167091 0 0 0.0084
## [87,] 0.00388539178 0.3836523 0 0 0.0068
## [88,] -0.00493843468 0.3963384 0 0 0.0072
## [89,] -0.02243857389 0.7723703 0 0 0.0084
## [90,] -0.00131422721 0.6432415 0 0 0.0084
## [91,] -0.01014894246 0.6755473 0 0 0.0060
## [92,] -0.01535781204 0.4919176 0 0 0.0068
## [93,] -0.00405443910 0.6134439 0 0 0.0056
## [94,] 0.02397694021 0.8350158 0 0 0.0092
## [95,] 0.03323071355 1.1205607 0 0 0.0088
## [96,] -0.01460856492 0.6602766 0 0 0.0080
## [97,] -0.01611234035 0.8623309 0 0 0.0072
## [98,] -0.00992605768 0.3032675 0 0 0.0056
## [99,] 0.00293467104 0.4275392 0 0 0.0064
## [100,] -0.00315029049 0.1493092 0 0 0.0064
## [101,] -0.02414928674 0.4740498 0 0 0.0060
## [102,] -0.01196833794 0.4277449 0 0 0.0064
## [103,] 0.00702737857 0.3458264 0 0 0.0044
## [104,] 0.00081247148 0.5087077 0 0 0.0088
## [105,] -0.04098369641 1.0601524 0 0 0.0064
## [106,] 0.06037070908 1.2591236 0 0 0.0076
## [107,] 0.12126752835 2.3940693 0 0 0.0116
## [108,] -0.02577292465 0.7680420 0 0 0.0092
## [109,] -0.01375276917 0.5530215 0 0 0.0076
## [110,] -0.00880519581 0.3398481 0 0 0.0060
## [111,] -0.00759717373 0.2619526 0 0 0.0036
## [112,] -0.10419431337 1.8206243 0 0 0.0084
## [113,] -0.03256260458 0.7349917 0 0 0.0096
## [114,] -0.00930695928 0.4708937 0 0 0.0076
## [115,] 0.00051492548 0.2879521 0 0 0.0040
## [116,] -0.00868797392 0.4236639 0 0 0.0064
## [117,] -0.06950302971 0.9904528 0 0 0.0084
## [118,] -0.00097697569 0.7214163 0 0 0.0084
## [119,] -0.00545746211 0.2800523 0 0 0.0056
## [120,] -0.01503763184 0.5584113 0 0 0.0096
## [121,] -0.02491833250 0.4644428 0 0 0.0076
## [122,] -0.01825176065 0.7168326 0 0 0.0080
## [123,] 0.00025325545 0.4590183 0 0 0.0072
## [124,] 0.03279933360 1.0473740 0 0 0.0092
## [125,] -0.00626008750 0.5059183 0 0 0.0068
## [126,] 0.02766024658 0.9681095 0 0 0.0080
## [127,] 0.00144914331 0.3769731 0 0 0.0080
## [128,] 0.01345583162 0.7735084 0 0 0.0044
## [129,] 0.00511791768 0.3988761 0 0 0.0080
## [130,] 0.00126558860 0.4417102 0 0 0.0056
## [131,] 0.11522493819 2.2388762 0 0 0.0088
## [132,] -0.00390198832 0.4878489 0 0 0.0064
## [133,] 0.44786958325 5.0399004 0 0 0.0152
## [134,] 0.08948031525 1.7728465 0 0 0.0076
## [135,] 0.08447585951 1.4827339 0 0 0.0132
## [136,] -0.01689404247 0.4408685 0 0 0.0068
## [137,] -0.02389772099 0.4266962 0 0 0.0048
## [138,] -0.02423098692 0.9099016 0 0 0.0116
## [139,] -0.05675219485 1.0223701 0 0 0.0096
## [140,] -0.07617943285 1.7256562 0 0 0.0072
## [141,] -0.03070713763 0.7938384 0 0 0.0076
## [142,] -0.04283266012 0.6689414 0 0 0.0112
## [143,] -0.00584929603 0.4601078 0 0 0.0080
## [144,] -0.01049222166 0.3128142 0 0 0.0064
## [145,] -0.02434740743 0.4429757 0 0 0.0060
## [146,] -0.03197249427 0.9190140 0 0 0.0096
## [147,] -0.02321395829 0.4679094 0 0 0.0068
## [148,] -0.00802865988 0.4449684 0 0 0.0076
## [149,] -0.10420371941 1.4692283 0 0 0.0112
## [150,] -0.00232470807 0.2839659 0 0 0.0052
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## [474,] -0.04990249692 1.2050945 0 0 0.0104
## [475,] -0.06026107956 1.3795509 0 0 0.0100
## [476,] 0.13725739813 2.6491498 0 0 0.0088
## [477,] -0.06222008313 1.5226899 0 0 0.0136
## [478,] 0.03163125838 0.9988847 0 0 0.0088
## [479,] -0.01738078966 0.4925509 0 0 0.0076
## [480,] -0.01705485665 0.4853933 0 0 0.0056
## [481,] -0.02171048896 0.6540417 0 0 0.0072
## [482,] -0.01011931363 0.3098851 0 0 0.0064
## [483,] -0.02630471017 0.6708100 0 0 0.0044
## [484,] -0.01908815633 0.5496103 0 0 0.0068
## [485,] -0.01239970435 0.3112727 0 0 0.0072
## [486,] -0.00942721232 0.3526367 0 0 0.0056
## [487,] 0.01740798191 0.3633009 0 0 0.0052
## [488,] -0.05389333445 1.3694555 0 0 0.0076
## [489,] 0.10336384146 3.7683566 0 0 0.0104
## [490,] 0.04647292882 3.7944616 0 0 0.0092
## [491,] 0.00920877933 0.7421756 0 0 0.0088
## [492,] -0.01476542301 0.3709889 0 0 0.0064
## [493,] -0.03201084789 1.4906171 0 0 0.0092
## [494,] -0.73779421386 15.9689764 0 0 0.0096
## [495,] -0.01453841031 0.3873425 0 0 0.0064
## [496,] 0.01361413384 0.4767649 0 0 0.0072
## [497,] 0.00670428082 0.6974593 0 0 0.0052
## [498,] -0.00162987159 0.4187843 0 0 0.0088
## [499,] 0.01647693825 1.6562493 0 0 0.0048
## [500,] 0.00553612848 0.4173081 0 0 0.0076
## [501,] -0.08837687669 1.8860368 0 0 0.0112
## [502,] 0.01269879265 0.6887290 0 0 0.0052
## [503,] -0.00047915884 0.7483503 0 0 0.0100
## [504,] -0.02222443239 0.5514601 0 0 0.0068
## [505,] -0.03942132433 0.8887575 0 0 0.0088
## [506,] -0.04390457260 0.8683602 0 0 0.0076
## [507,] -0.09459992156 1.5045282 0 0 0.0104
## [508,] -0.05262292770 1.3950307 0 0 0.0064
## [509,] -0.11623264994 2.0848351 0 0 0.0092
## [510,] 0.00666961157 0.7974243 0 0 0.0064
## [511,] -0.00066745885 0.7506671 0 0 0.0104
## [512,] -0.02720921903 0.7169747 0 0 0.0084
## [513,] 0.02732282608 0.9799230 0 0 0.0040
## [514,] -0.01482058457 0.4300315 0 0 0.0124
## [515,] 0.07136260577 2.4955321 0 0 0.0072
## [516,] 0.00869263420 0.7185167 0 0 0.0048
## [517,] -0.03740269326 1.8364442 0 0 0.0100
## [518,] -0.00646600831 0.5057158 0 0 0.0076
## [519,] -0.00393633960 0.3243712 0 0 0.0080
## [520,] -0.06779450741 4.3024564 0 0 0.0068
## [521,] -0.13505184577 3.4411022 0 0 0.0120
## [522,] 0.03481352543 1.5127844 0 0 0.0060
## [523,] 0.01547423052 1.1154718 0 0 0.0072
## [524,] -0.01491747957 0.7447249 0 0 0.0084
## [525,] -0.02565500250 0.7679012 0 0 0.0072
## [526,] -0.03475021493 0.9498661 0 0 0.0088
## [527,] 0.02024462896 1.1044354 0 0 0.0088
## [528,] 0.02780250458 0.9020932 0 0 0.0056
## [529,] -0.07114680406 2.1625858 0 0 0.0088
## [530,] -0.00786664820 1.3100537 0 0 0.0100
## [531,] -0.02469880936 1.0071071 0 0 0.0072
## [532,] 0.00705780508 0.5459288 0 0 0.0080
## [533,] -0.17113193693 3.0294850 0 0 0.0124
## [534,] -0.01032987394 0.4506866 0 0 0.0060
## [535,] -0.01655348159 0.9461312 0 0 0.0088
## [536,] 0.01390265210 1.2454607 0 0 0.0092
## [537,] -0.05928322349 1.1828984 0 0 0.0084
## [538,] -0.02867543360 0.5306067 0 0 0.0072
## [539,] 0.00291097226 0.9753376 0 0 0.0076
## [540,] 0.01302001963 0.6648716 0 0 0.0052
## [541,] 0.00081379178 0.6835970 0 0 0.0068
## [542,] -0.01344093170 0.7984617 0 0 0.0064
## [543,] 0.00581183427 0.5823829 0 0 0.0056
## [544,] -0.00630216288 0.4170238 0 0 0.0072
## [545,] -0.02948462593 0.7597981 0 0 0.0068
## [546,] -0.03249944295 0.7962682 0 0 0.0092
## [547,] 0.00447927246 0.8929101 0 0 0.0112
## [548,] -0.01702659127 0.6070707 0 0 0.0068
## [549,] -0.02213391448 1.1702346 0 0 0.0068
## [550,] -0.04410959008 0.8953039 0 0 0.0108
## [551,] -0.02544671258 0.6385921 0 0 0.0064
## [552,] 0.01723341929 0.6836433 0 0 0.0064
## [553,] -0.07768406563 1.2853261 0 0 0.0112
## [554,] 0.22696200311 3.7763758 0 0 0.0108
## [555,] -0.05090856082 1.8910760 0 0 0.0096
## [556,] -0.03934105397 1.0744375 0 0 0.0092
## [557,] 0.00808619619 1.6547902 0 0 0.0084
## [558,] 0.01999788591 1.2412699 0 0 0.0080
## [559,] 0.01754462575 0.6596200 0 0 0.0088
## [560,] 0.02501772432 0.6855490 0 0 0.0060
## [561,] -0.03812673552 1.1100549 0 0 0.0096
## [562,] -0.02488635536 0.8361212 0 0 0.0060
## [563,] -0.05716541986 1.1559345 0 0 0.0128
## [564,] -0.01833210642 0.4417288 0 0 0.0052
## [565,] -0.05479731225 1.8128083 0 0 0.0088
## [566,] -0.00346018475 0.5154745 0 0 0.0080
## [567,] -0.05639922053 1.6903785 0 0 0.0096
## [568,] -0.09915916157 2.3922946 0 0 0.0092
## [569,] -0.01379666828 0.7279852 0 0 0.0084
## [570,] -0.07647728007 1.9730866 0 0 0.0068
## [571,] -0.11995871485 3.2182572 0 0 0.0076
## [572,] -0.04716490117 2.2461903 0 0 0.0084
## [573,] -0.03297362496 0.8258754 0 0 0.0080
## [574,] -0.06118354547 1.3645460 0 0 0.0076
## [575,] -0.05193320088 1.2161553 0 0 0.0072
## [576,] 0.01058485344 1.0071614 0 0 0.0088
## [577,] -0.28231449345 4.4437050 0 0 0.0156
## [578,] -0.04319518803 1.1249487 0 0 0.0104
## [579,] -0.08583256261 2.5055900 0 0 0.0116
## [580,] 0.00928642354 0.9746270 0 0 0.0056
## [581,] -0.05945509169 1.7720413 0 0 0.0080
## [582,] -0.00612618147 0.2295534 0 0 0.0036
## [583,] -0.00041429543 0.5070291 0 0 0.0088
## [584,] 0.00185863786 0.7700441 0 0 0.0072
## [585,] -0.00658084255 0.4887282 0 0 0.0076
## [586,] 0.01232722948 0.5786548 0 0 0.0056
## [587,] -0.26830092194 3.7776721 0 0 0.0128
## [588,] -0.02748815889 1.7272527 0 0 0.0072
## [589,] -0.12900990957 2.6940778 0 0 0.0112
## [590,] -0.01795080304 0.5009195 0 0 0.0056
## [591,] 0.01518059463 0.4980846 0 0 0.0060
## [592,] 0.01484701089 1.3012187 0 0 0.0084
## [593,] -0.03244572248 0.9177138 0 0 0.0072
## [594,] -0.05647749037 1.9045405 0 0 0.0068
## [595,] -0.01263020201 0.5300704 0 0 0.0084
## [596,] -0.03435471657 0.7804876 0 0 0.0084
## [597,] -0.01768149956 1.0220295 0 0 0.0072
## [598,] -0.01535088140 0.4099797 0 0 0.0060
## [599,] -0.00877185722 0.5517931 0 0 0.0052
## [600,] 0.00325876686 0.5392237 0 0 0.0088
## [601,] -0.21523943918 4.2251819 0 0 0.0116
## [602,] -0.02821227170 0.9005946 0 0 0.0068
## [603,] -0.00779339916 0.5947470 0 0 0.0072
## [604,] -0.00392023967 1.2001194 0 0 0.0088
## [605,] -0.08566468495 1.6555774 0 0 0.0084
## [606,] 0.11945650885 2.4262816 0 0 0.0092
## [607,] -0.07813844928 1.5353022 0 0 0.0072
## [608,] -0.00510309489 0.8381410 0 0 0.0092
## [609,] -0.00340886981 1.2335609 0 0 0.0064
## [610,] -0.01795463319 0.7861776 0 0 0.0048
## [611,] -0.00744933597 0.4417312 0 0 0.0048
## [612,] 0.00388041737 0.4252053 0 0 0.0064
## [613,] -0.02550732215 0.6824725 0 0 0.0072
## [614,] -0.04026289223 0.9149887 0 0 0.0096
## [615,] -0.01357674620 0.3795332 0 0 0.0060
## [616,] -0.01784003223 0.4220378 0 0 0.0064
## [617,] -0.03068044300 0.7235531 0 0 0.0116
## [618,] -0.01688368860 1.0946480 0 0 0.0088
## [619,] 0.00059270655 0.6299292 0 0 0.0072
## [620,] 0.00586891679 1.3111318 0 0 0.0080
## [621,] 0.00292149451 0.3975609 0 0 0.0080
## [622,] -0.06144993859 1.3092823 0 0 0.0088
## [623,] -0.05770495564 1.7539533 0 0 0.0080
## [624,] -0.08312567494 3.0244135 0 0 0.0076
## [625,] -0.00019458838 0.3711538 0 0 0.0040
## [626,] 0.02662832045 0.8630005 0 0 0.0064
## [627,] -0.08075095054 1.5143306 0 0 0.0100
## [628,] -0.00549733442 0.5172497 0 0 0.0064
## [629,] -0.09426243847 2.0207528 0 0 0.0068
## [630,] -0.05346885809 1.0244725 0 0 0.0136
## [631,] -0.07205332997 2.2374875 0 0 0.0096
## [632,] 0.19773194802 3.4655173 0 0 0.0108
## [633,] -0.05823052060 1.3983702 0 0 0.0084
## [634,] -0.02355776117 0.8347774 0 0 0.0052
## [635,] -0.00795378206 0.3313058 0 0 0.0044
## [636,] 0.00453365770 0.4919846 0 0 0.0048
## [637,] -0.01881257337 0.6282906 0 0 0.0064
## [638,] -0.02453461688 0.4978605 0 0 0.0068
## [639,] -0.01674137492 0.5105064 0 0 0.0060
## [640,] -0.03510867989 0.5816163 0 0 0.0068
## [641,] -0.07193073403 1.1201310 0 0 0.0112
## [642,] 0.01551443884 0.6573726 0 0 0.0068
## [643,] -0.03041550250 0.7508427 0 0 0.0092
## [644,] -0.04481394151 2.3885358 0 0 0.0076
## [645,] 0.00963390673 1.7152012 0 0 0.0096
## [646,] -0.03503125691 1.0448565 0 0 0.0096
## [647,] 0.03040614981 1.5875663 0 0 0.0064
## [648,] -0.02683469105 0.5904054 0 0 0.0092
## [649,] -0.01088160897 1.1736270 0 0 0.0080
## [650,] -0.02058211611 0.4677316 0 0 0.0056
## [651,] 0.04283203256 1.8765122 0 0 0.0124
## [652,] -0.00126246304 0.6584181 0 0 0.0076
## [653,] -0.01231690436 0.5908343 0 0 0.0064
## [654,] 0.00284019897 0.8361066 0 0 0.0060
## [655,] -0.01345065152 2.1896876 0 0 0.0096
## [656,] 0.01076277742 0.6625391 0 0 0.0056
## [657,] -0.32885065034 5.0224256 0 0 0.0136
## [658,] 0.82852899629 9.0863564 0 0 0.0152
## [659,] -0.04682066314 1.1746644 0 0 0.0068
## [660,] -0.02368944365 0.8336448 0 0 0.0088
## [661,] -0.02464555303 0.9569493 0 0 0.0076
## [662,] 0.01780628346 1.3442671 0 0 0.0076
## [663,] -0.06544736531 1.1296142 0 0 0.0092
## [664,] -0.03617788916 0.7566387 0 0 0.0088
## [665,] -0.04996283617 1.5369428 0 0 0.00724.5.4 Predict fitted values for each individual
pred.npb4 <- predict(fit.npb4)
fittedvals4 <- pred.npb4$fitted.vals4.5.5 Plot predicted outcomes against “measured” outcomes
plot(fittedvals4, Y)
abline(a = 0, b = 1, col = "red")
5 Linear models for each predictor
5.1 Screening the exposures
Here I’m going to loop through some linear regression models to see if anything shows up here. Remember that the exposure and covariates have all been scaled.
The standard deviation of the mean_o3 variable is 3.06 ppb
lm_results <- data.frame()
for(i in 1:length(colnames(X.scaled))) {
lm_df <- as.data.frame(cbind(Y, X.scaled[,i], W.scaled2))
names(lm_df)[2] <- colnames(X.scaled)[i]
ad_lm <- lm(birth_weight ~ ., data = lm_df)
temp <- data.frame(exp = colnames(X.scaled)[i],
beta = summary(ad_lm)$coefficients[2,1],
beta.se = summary(ad_lm)$coefficients[2,2],
p.value = summary(ad_lm)$coefficients[2,4])
temp$lcl <- temp$beta - 1.96*temp$beta.se
temp$ucl <- temp$beta + 1.96*temp$beta.se
lm_results <- bind_rows(lm_results, temp)
rm(temp)
}
lm_resultswrite_csv(lm_results, here::here("Results", "LM_Effects_Birth_Weight_v4.csv"))6 Linear model with the ozone and temperature predictors
The standard deviation of the mean_o3 variable is 3.06 ppb The standard deviation of the mean_temp variable is 4.54 degrees F
lm_df <- as.data.frame(cbind(Y, X.scaled[, c("mean_o3", "mean_temp")], W.scaled2))
names(lm_df)## [1] "birth_weight" "mean_o3" "mean_temp" "lat"
## [5] "lon" "lat_lon_int" "latina_re" "black_re"
## [9] "other_re" "ed_no_hs" "ed_hs" "ed_aa"
## [13] "ed_4yr" "low_bmi" "ovwt_bmi" "obese_bmi"
## [17] "concep_spring" "concep_summer" "concep_fall" "concep_2010"
## [21] "concep_2011" "concep_2012" "concep_2013" "maternal_age"
## [25] "any_smoker" "smokeSH" "mean_cpss" "mean_epsd"
## [29] "male"#names(lm_df)[2] <- "mean_o3"
head(lm_df)bw_lm <- lm(birth_weight ~ mean_o3 + mean_temp + mean_o3*mean_temp +
lat + lon + lat_lon_int +
latina_re + black_re + other_re +
ed_no_hs + ed_hs + ed_aa + ed_4yr +
low_bmi + ovwt_bmi + obese_bmi +
concep_spring + concep_summer + concep_fall +
concep_2010 + concep_2011 + concep_2012 + concep_2013 +
maternal_age + any_smoker + smokeSH +
mean_cpss + mean_epsd + male,
data = lm_df)
summary(bw_lm)##
## Call:
## lm(formula = birth_weight ~ mean_o3 + mean_temp + mean_o3 * mean_temp +
## lat + lon + lat_lon_int + latina_re + black_re + other_re +
## ed_no_hs + ed_hs + ed_aa + ed_4yr + low_bmi + ovwt_bmi +
## obese_bmi + concep_spring + concep_summer + concep_fall +
## concep_2010 + concep_2011 + concep_2012 + concep_2013 + maternal_age +
## any_smoker + smokeSH + mean_cpss + mean_epsd + male, data = lm_df)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1949.66 -299.30 32.42 320.13 1391.98
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 2951.708 484.042 6.098 0.00000000162 ***
## mean_o3 -111.550 53.782 -2.074 0.03836 *
## mean_temp 84.775 53.297 1.591 0.11206
## lat 39.445 17353.487 0.002 0.99819
## lon 3.946 8171.897 0.000 0.99961
## lat_lon_int 51.064 20965.561 0.002 0.99806
## latina_re -101.910 46.323 -2.200 0.02807 *
## black_re -291.040 49.984 -5.823 0.00000000815 ***
## other_re -98.104 67.067 -1.463 0.14389
## ed_no_hs 158.566 75.327 2.105 0.03558 *
## ed_hs 135.453 67.217 2.015 0.04420 *
## ed_aa 76.692 59.249 1.294 0.19587
## ed_4yr 88.459 49.852 1.774 0.07634 .
## low_bmi -82.355 90.617 -0.909 0.36369
## ovwt_bmi 42.942 39.431 1.089 0.27644
## obese_bmi 122.909 44.537 2.760 0.00591 **
## concep_spring -151.372 57.096 -2.651 0.00817 **
## concep_summer -84.097 74.042 -1.136 0.25635
## concep_fall 2.543 70.975 0.036 0.97143
## concep_2010 307.856 485.074 0.635 0.52582
## concep_2011 300.403 485.844 0.618 0.53653
## concep_2012 394.746 487.939 0.809 0.41873
## concep_2013 380.787 485.067 0.785 0.43266
## maternal_age 57.432 21.591 2.660 0.00796 **
## any_smoker -151.703 62.418 -2.430 0.01528 *
## smokeSH -74.770 43.616 -1.714 0.08684 .
## mean_cpss 3.557 19.365 0.184 0.85430
## mean_epsd -46.277 19.680 -2.352 0.01892 *
## male 174.141 31.857 5.466 0.00000006010 ***
## mean_o3:mean_temp -151.446 16.515 -9.170 < 0.0000000000000002 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 470.2 on 867 degrees of freedom
## Multiple R-squared: 0.2284, Adjusted R-squared: 0.2025
## F-statistic: 8.847 on 29 and 867 DF, p-value: < 0.00000000000000022plot(bw_lm)## Warning: not plotting observations with leverage one:
## 1
7 Try a GAM with the ozone and temperature predictor
The NPB model above indicates that there might be a signal for ozone. None of the other exposures had a PIP > 0.5. Here I’ve got a GAM with a smoothing term for ozone and temperature to see about potential nonlinear effects
The mean and standard deviation of the mean_o3 variable are 47.96 (3.06) ppb The mean and standard deviation of the mean_temp variable is 52.58 (4.54) degrees F
library(mgcv)## Loading required package: nlme##
## Attaching package: 'nlme'## The following object is masked from 'package:dplyr':
##
## collapse## This is mgcv 1.8-34. For overview type 'help("mgcv-package")'.library(tidymv)
gam_df <- as.data.frame(cbind(Y, X.scaled[, c("mean_o3", "mean_temp")], W.scaled2))
names(gam_df)## [1] "birth_weight" "mean_o3" "mean_temp" "lat"
## [5] "lon" "lat_lon_int" "latina_re" "black_re"
## [9] "other_re" "ed_no_hs" "ed_hs" "ed_aa"
## [13] "ed_4yr" "low_bmi" "ovwt_bmi" "obese_bmi"
## [17] "concep_spring" "concep_summer" "concep_fall" "concep_2010"
## [21] "concep_2011" "concep_2012" "concep_2013" "maternal_age"
## [25] "any_smoker" "smokeSH" "mean_cpss" "mean_epsd"
## [29] "male"#names(gam_df)[2] <- "mean_o3"
head(gam_df)bw_gam <- gam(birth_weight ~ s(mean_o3, mean_temp) +
lat + lon + lat_lon_int +
latina_re + black_re + other_re +
ed_no_hs + ed_hs + ed_aa + ed_4yr +
low_bmi + ovwt_bmi + obese_bmi +
concep_spring + concep_summer + concep_fall +
concep_2010 + concep_2011 + concep_2012 + concep_2013 +
maternal_age + any_smoker + smokeSH +
mean_cpss + mean_epsd + male,
data = gam_df, method = "REML")
gam.check(bw_gam)
##
## Method: REML Optimizer: outer newton
## full convergence after 5 iterations.
## Gradient range [-0.003901862,0.0002318709]
## (score 6612.104 & scale 198536.5).
## Hessian positive definite, eigenvalue range [6.271652,434.1997].
## Model rank = 56 / 56
##
## Basis dimension (k) checking results. Low p-value (k-index<1) may
## indicate that k is too low, especially if edf is close to k'.
##
## k' edf k-index p-value
## s(mean_o3,mean_temp) 29.0 20.3 1.02 0.73summary(bw_gam)##
## Family: gaussian
## Link function: identity
##
## Formula:
## birth_weight ~ s(mean_o3, mean_temp) + lat + lon + lat_lon_int +
## latina_re + black_re + other_re + ed_no_hs + ed_hs + ed_aa +
## ed_4yr + low_bmi + ovwt_bmi + obese_bmi + concep_spring +
## concep_summer + concep_fall + concep_2010 + concep_2011 +
## concep_2012 + concep_2013 + maternal_age + any_smoker + smokeSH +
## mean_cpss + mean_epsd + male
##
## Parametric coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 2672.485 463.780 5.762 0.00000001159 ***
## lat 1969.493 16669.709 0.118 0.90598
## lon -899.973 7850.164 -0.115 0.90875
## lat_lon_int 2378.919 20139.472 0.118 0.90600
## latina_re -93.390 44.358 -2.105 0.03555 *
## black_re -282.806 47.713 -5.927 0.00000000447 ***
## other_re -84.252 64.088 -1.315 0.18899
## ed_no_hs 127.350 72.093 1.766 0.07768 .
## ed_hs 105.756 64.554 1.638 0.10174
## ed_aa 73.939 56.623 1.306 0.19197
## ed_4yr 77.556 47.667 1.627 0.10410
## low_bmi -125.792 86.718 -1.451 0.14727
## ovwt_bmi 54.344 37.778 1.439 0.15066
## obese_bmi 107.672 42.678 2.523 0.01182 *
## concep_spring -115.526 62.210 -1.857 0.06365 .
## concep_summer -212.023 91.687 -2.312 0.02099 *
## concep_fall -78.197 89.775 -0.871 0.38398
## concep_2010 535.014 467.861 1.144 0.25314
## concep_2011 475.483 468.750 1.014 0.31070
## concep_2012 643.518 470.386 1.368 0.17165
## concep_2013 582.557 468.024 1.245 0.21358
## maternal_age 60.560 20.658 2.932 0.00346 **
## any_smoker -154.503 59.686 -2.589 0.00980 **
## smokeSH -63.289 41.579 -1.522 0.12835
## mean_cpss 2.203 18.589 0.119 0.90568
## mean_epsd -45.229 18.829 -2.402 0.01651 *
## male 157.454 30.433 5.174 0.00000028641 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Approximate significance of smooth terms:
## edf Ref.df F p-value
## s(mean_o3,mean_temp) 20.3 25.08 7.64 <0.0000000000000002 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## R-sq.(adj) = 0.284 Deviance explained = 32.1%
## -REML = 6612.1 Scale est. = 1.9854e+05 n = 897save(gam_df, bw_gam, file = here::here("Results", "BW_GAM_v4.rdata"))library(mgcViz)## Loading required package: qgam## Loading required package: rgl## Registered S3 method overwritten by 'GGally':
## method from
## +.gg ggplot2## Registered S3 method overwritten by 'mgcViz':
## method from
## +.gg GGally##
## Attaching package: 'mgcViz'## The following objects are masked from 'package:stats':
##
## qqline, qqnorm, qqplotgam_b <- getViz(bw_gam)
plot(sm(gam_b, 1)) +
l_fitRaster() + l_fitContour() + l_points() +
labs(title = NULL, x = "Ozone (scaled)", y = "Temperature (scaled)") +
guides(fill=guide_legend(title="Change in\nbirth weight (g)")) +
ggsave(filename = here::here("Figs", "Ozone_Temp_GAM_Birth_Weight_v4.jpeg"),
device = "jpeg", width = 5, height = 3, units = "in", dpi = 500) 
8 GAM Sensitivity Analysis
The previous GAM suggested a possible nonlinear relationship between ozone and birth weight. However, this might be the influence of abnormally high and low exposures.
Therefore, Ander suggested a sensitivity analysis where we excluded the top and bottom 2.5% of data and just use the middle 95%.
library(mgcv)
gam_df <- as.data.frame(cbind(Y, X.scaled[, c("mean_o3", "mean_temp")], W.scaled2))
names(gam_df)## [1] "birth_weight" "mean_o3" "mean_temp" "lat"
## [5] "lon" "lat_lon_int" "latina_re" "black_re"
## [9] "other_re" "ed_no_hs" "ed_hs" "ed_aa"
## [13] "ed_4yr" "low_bmi" "ovwt_bmi" "obese_bmi"
## [17] "concep_spring" "concep_summer" "concep_fall" "concep_2010"
## [21] "concep_2011" "concep_2012" "concep_2013" "maternal_age"
## [25] "any_smoker" "smokeSH" "mean_cpss" "mean_epsd"
## [29] "male"head(gam_df)gam_df2 <- gam_df %>%
filter(mean_o3 > -2 & mean_o3 < 2) %>%
filter(mean_temp > -2 & mean_temp < 2)
hist(gam_df2$mean_o3)
hist(gam_df2$mean_temp)
bw_gam2 <- gam(birth_weight ~ s(mean_o3, mean_temp) +
lat + lon + lat_lon_int +
latina_re + black_re + other_re +
ed_no_hs + ed_hs + ed_aa + ed_4yr +
low_bmi + ovwt_bmi + obese_bmi +
concep_spring + concep_summer + concep_fall +
concep_2010 + concep_2011 + concep_2012 + concep_2013 +
maternal_age + any_smoker + smokeSH +
mean_cpss + mean_epsd + male,
data = gam_df2, method = "REML")
gam.check(bw_gam2)
##
## Method: REML Optimizer: outer newton
## full convergence after 6 iterations.
## Gradient range [-0.00000008175124,0.000000001043013]
## (score 6455.826 & scale 197464).
## Hessian positive definite, eigenvalue range [2.947887,424.5697].
## Model rank = 56 / 56
##
## Basis dimension (k) checking results. Low p-value (k-index<1) may
## indicate that k is too low, especially if edf is close to k'.
##
## k' edf k-index p-value
## s(mean_o3,mean_temp) 29.0 12.8 1.02 0.69summary(bw_gam2)##
## Family: gaussian
## Link function: identity
##
## Formula:
## birth_weight ~ s(mean_o3, mean_temp) + lat + lon + lat_lon_int +
## latina_re + black_re + other_re + ed_no_hs + ed_hs + ed_aa +
## ed_4yr + low_bmi + ovwt_bmi + obese_bmi + concep_spring +
## concep_summer + concep_fall + concep_2010 + concep_2011 +
## concep_2012 + concep_2013 + maternal_age + any_smoker + smokeSH +
## mean_cpss + mean_epsd + male
##
## Parametric coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 2757.43 461.13 5.980 0.00000000331 ***
## lat 6394.80 16840.59 0.380 0.70425
## lon -2991.04 7930.73 -0.377 0.70616
## lat_lon_int 7724.85 20346.00 0.380 0.70428
## latina_re -113.84 44.46 -2.561 0.01062 *
## black_re -288.02 47.86 -6.018 0.00000000264 ***
## other_re -91.52 64.36 -1.422 0.15543
## ed_no_hs 150.48 72.28 2.082 0.03766 *
## ed_hs 125.31 64.64 1.939 0.05287 .
## ed_aa 91.76 56.90 1.613 0.10722
## ed_4yr 86.82 47.99 1.809 0.07081 .
## low_bmi -123.30 86.28 -1.429 0.15337
## ovwt_bmi 49.69 38.06 1.306 0.19205
## obese_bmi 101.48 42.97 2.362 0.01840 *
## concep_spring -90.04 61.27 -1.470 0.14203
## concep_summer -167.34 87.73 -1.907 0.05680 .
## concep_fall -58.98 85.36 -0.691 0.48980
## concep_2010 463.35 464.50 0.998 0.31879
## concep_2011 407.37 465.27 0.876 0.38152
## concep_2012 543.76 467.05 1.164 0.24466
## concep_2013 514.05 464.70 1.106 0.26896
## maternal_age 61.12 20.74 2.947 0.00329 **
## any_smoker -162.02 59.74 -2.712 0.00683 **
## smokeSH -78.62 41.90 -1.876 0.06099 .
## mean_cpss 5.43 18.68 0.291 0.77134
## mean_epsd -46.95 18.91 -2.483 0.01322 *
## male 148.06 30.64 4.832 0.00000160761 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Approximate significance of smooth terms:
## edf Ref.df F p-value
## s(mean_o3,mean_temp) 12.84 17.44 2.622 0.000321 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## R-sq.(adj) = 0.181 Deviance explained = 21.7%
## -REML = 6455.8 Scale est. = 1.9746e+05 n = 878save(gam_df2, bw_gam2, file = here::here("Results", "BW_GAM_Sensitivity_v4.rdata"))library(mgcViz)
gam_b2 <- getViz(bw_gam2)
plot(sm(gam_b2, 1)) +
l_fitRaster() + l_fitContour() + l_points() +
labs(title = NULL, x = "Ozone (scaled)", y = "Temperature (scaled)") +
guides(fill=guide_legend(title="Change in\nbirth weight (g)"))
ggsave(filename = here::here("Figs", "Ozone_Temp_GAM_Birth_Weight_Sensitivity_v4.jpeg"),
device = "jpeg", width = 5, height = 3, units = "in", dpi = 500)